---
_id: '8175'
abstract:
- lang: eng
  text: We study edge asymptotics of poissonized Plancherel-type measures on skew
    Young diagrams (integer partitions). These measures can be seen as generalizations
    of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's
    problem on longest increasing subsequences of random permutations and the last
    passage percolation (corner growth) discrete versions thereof. Moreover they interpolate
    between said measures and the uniform measure on partitions. In the new KPZ-like
    1/3 exponent edge scaling limit with logarithmic corrections, we find new probability
    distributions generalizing the classical Tracy--Widom GUE, GOE and GSE distributions
    from the theory of random matrices.
acknowledgement: "D.B. is especially grateful to Patrik Ferrari for suggesting simplifications
  in Section 3 and\r\nto Alessandra Occelli for suggesting the name for the models
  of Section 2.\r\n"
article_number: '34'
article_processing_charge: No
arxiv: 1
author:
- first_name: Dan
  full_name: Betea, Dan
  last_name: Betea
- first_name: Jérémie
  full_name: Bouttier, Jérémie
  last_name: Bouttier
- first_name: Peter
  full_name: Nejjar, Peter
  id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
  last_name: Nejjar
- first_name: Mirjana
  full_name: Vuletíc, Mirjana
  last_name: Vuletíc
citation:
  ama: 'Betea D, Bouttier J, Nejjar P, Vuletíc M. New edge asymptotics of skew Young
    diagrams via free boundaries. In: <i>Proceedings on the 31st International Conference
    on Formal Power Series and Algebraic Combinatorics</i>. Formal Power Series and
    Algebraic Combinatorics; 2019.'
  apa: 'Betea, D., Bouttier, J., Nejjar, P., &#38; Vuletíc, M. (2019). New edge asymptotics
    of skew Young diagrams via free boundaries. In <i>Proceedings on the 31st International
    Conference on Formal Power Series and Algebraic Combinatorics</i>. Ljubljana,
    Slovenia: Formal Power Series and Algebraic Combinatorics.'
  chicago: Betea, Dan, Jérémie Bouttier, Peter Nejjar, and Mirjana Vuletíc. “New Edge
    Asymptotics of Skew Young Diagrams via Free Boundaries.” In <i>Proceedings on
    the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>.
    Formal Power Series and Algebraic Combinatorics, 2019.
  ieee: D. Betea, J. Bouttier, P. Nejjar, and M. Vuletíc, “New edge asymptotics of
    skew Young diagrams via free boundaries,” in <i>Proceedings on the 31st International
    Conference on Formal Power Series and Algebraic Combinatorics</i>, Ljubljana,
    Slovenia, 2019.
  ista: 'Betea D, Bouttier J, Nejjar P, Vuletíc M. 2019. New edge asymptotics of skew
    Young diagrams via free boundaries. Proceedings on the 31st International Conference
    on Formal Power Series and Algebraic Combinatorics. FPSAC: International Conference
    on Formal Power Series and Algebraic Combinatorics, 34.'
  mla: Betea, Dan, et al. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.”
    <i>Proceedings on the 31st International Conference on Formal Power Series and
    Algebraic Combinatorics</i>, 34, Formal Power Series and Algebraic Combinatorics,
    2019.
  short: D. Betea, J. Bouttier, P. Nejjar, M. Vuletíc, in:, Proceedings on the 31st
    International Conference on Formal Power Series and Algebraic Combinatorics, Formal
    Power Series and Algebraic Combinatorics, 2019.
conference:
  end_date: 2019-07-05
  location: Ljubljana, Slovenia
  name: 'FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics'
  start_date: 2019-07-01
date_created: 2020-07-26T22:01:04Z
date_published: 2019-07-01T00:00:00Z
date_updated: 2021-01-12T08:17:18Z
day: '01'
department:
- _id: LaEr
ec_funded: 1
external_id:
  arxiv:
  - '1902.08750'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1902.08750
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
publication: Proceedings on the 31st International Conference on Formal Power Series
  and Algebraic Combinatorics
publication_status: published
publisher: Formal Power Series and Algebraic Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: New edge asymptotics of skew Young diagrams via free boundaries
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...
---
_id: '72'
abstract:
- lang: eng
  text: We consider the totally asymmetric simple exclusion process (TASEP) with non-random
    initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle
    initially at the origin. For ρ&lt;λ, there is a shock and the second class particle
    moves with speed 1−λ−ρ. For large time t, we show that the position of the second
    class particle fluctuates on a t1/3 scale and determine its limiting law. We also
    obtain the limiting distribution of the number of steps made by the second class
    particle until time t.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Patrick
  full_name: Ferrari, Patrick
  last_name: Ferrari
- first_name: Promit
  full_name: Ghosal, Promit
  last_name: Ghosal
- first_name: Peter
  full_name: Nejjar, Peter
  id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
  last_name: Nejjar
citation:
  ama: Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP
    with non-random initial condition. <i>Annales de l’institut Henri Poincare (B)
    Probability and Statistics</i>. 2019;55(3):1203-1225. doi:<a href="https://doi.org/10.1214/18-AIHP916">10.1214/18-AIHP916</a>
  apa: Ferrari, P., Ghosal, P., &#38; Nejjar, P. (2019). Limit law of a second class
    particle in TASEP with non-random initial condition. <i>Annales de l’institut
    Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics.
    <a href="https://doi.org/10.1214/18-AIHP916">https://doi.org/10.1214/18-AIHP916</a>
  chicago: Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second
    Class Particle in TASEP with Non-Random Initial Condition.” <i>Annales de l’institut
    Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics,
    2019. <a href="https://doi.org/10.1214/18-AIHP916">https://doi.org/10.1214/18-AIHP916</a>.
  ieee: P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle
    in TASEP with non-random initial condition,” <i>Annales de l’institut Henri Poincare
    (B) Probability and Statistics</i>, vol. 55, no. 3. Institute of Mathematical
    Statistics, pp. 1203–1225, 2019.
  ista: Ferrari P, Ghosal P, Nejjar P. 2019. Limit law of a second class particle
    in TASEP with non-random initial condition. Annales de l’institut Henri Poincare
    (B) Probability and Statistics. 55(3), 1203–1225.
  mla: Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with
    Non-Random Initial Condition.” <i>Annales de l’institut Henri Poincare (B) Probability
    and Statistics</i>, vol. 55, no. 3, Institute of Mathematical Statistics, 2019,
    pp. 1203–25, doi:<a href="https://doi.org/10.1214/18-AIHP916">10.1214/18-AIHP916</a>.
  short: P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B)
    Probability and Statistics 55 (2019) 1203–1225.
date_created: 2018-12-11T11:44:29Z
date_published: 2019-09-25T00:00:00Z
date_updated: 2023-10-17T08:53:45Z
day: '25'
department:
- _id: LaEr
- _id: JaMa
doi: 10.1214/18-AIHP916
ec_funded: 1
external_id:
  arxiv:
  - '1710.02323'
  isi:
  - '000487763200001'
intvolume: '        55'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1710.02323
month: '09'
oa: 1
oa_version: Preprint
page: 1203-1225
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_identifier:
  issn:
  - 0246-0203
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Limit law of a second class particle in TASEP with non-random initial condition
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2019'
...
---
_id: '70'
abstract:
- lang: eng
  text: We consider the totally asymmetric simple exclusion process in a critical
    scaling parametrized by a≥0, which creates a shock in the particle density of
    order aT−1/3, T the observation time. When starting from step initial data, we
    provide bounds on the limiting law which in particular imply that in the double
    limit lima→∞limT→∞ one recovers the product limit law and the degeneration of
    the correlation length observed at shocks of order 1. This result is shown to
    apply to a general last-passage percolation model. We also obtain bounds on the
    two-point functions of several airy processes.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Peter
  full_name: Nejjar, Peter
  id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
  last_name: Nejjar
citation:
  ama: Nejjar P. Transition to shocks in TASEP and decoupling of last passage times.
    <i>Latin American Journal of Probability and Mathematical Statistics</i>. 2018;15(2):1311-1334.
    doi:<a href="https://doi.org/10.30757/ALEA.v15-49">10.30757/ALEA.v15-49</a>
  apa: Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage
    times. <i>Latin American Journal of Probability and Mathematical Statistics</i>.
    Instituto Nacional de Matematica Pura e Aplicada. <a href="https://doi.org/10.30757/ALEA.v15-49">https://doi.org/10.30757/ALEA.v15-49</a>
  chicago: Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage
    Times.” <i>Latin American Journal of Probability and Mathematical Statistics</i>.
    Instituto Nacional de Matematica Pura e Aplicada, 2018. <a href="https://doi.org/10.30757/ALEA.v15-49">https://doi.org/10.30757/ALEA.v15-49</a>.
  ieee: P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,”
    <i>Latin American Journal of Probability and Mathematical Statistics</i>, vol.
    15, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1311–1334, 2018.
  ista: Nejjar P. 2018. Transition to shocks in TASEP and decoupling of last passage
    times. Latin American Journal of Probability and Mathematical Statistics. 15(2),
    1311–1334.
  mla: Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage
    Times.” <i>Latin American Journal of Probability and Mathematical Statistics</i>,
    vol. 15, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2018, pp. 1311–34,
    doi:<a href="https://doi.org/10.30757/ALEA.v15-49">10.30757/ALEA.v15-49</a>.
  short: P. Nejjar, Latin American Journal of Probability and Mathematical Statistics
    15 (2018) 1311–1334.
date_created: 2018-12-11T11:44:28Z
date_published: 2018-10-01T00:00:00Z
date_updated: 2023-10-10T13:11:29Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
- _id: JaMa
doi: 10.30757/ALEA.v15-49
ec_funded: 1
external_id:
  arxiv:
  - '1705.08836'
  isi:
  - '000460475800022'
file:
- access_level: open_access
  checksum: 2ded46aa284a836a8cbb34133a64f1cb
  content_type: application/pdf
  creator: kschuh
  date_created: 2019-02-14T09:44:10Z
  date_updated: 2020-07-14T12:47:46Z
  file_id: '5981'
  file_name: 2018_ALEA_Nejjar.pdf
  file_size: 394851
  relation: main_file
file_date_updated: 2020-07-14T12:47:46Z
has_accepted_license: '1'
intvolume: '        15'
isi: 1
issue: '2'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1311-1334
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
publication: Latin American Journal of Probability and Mathematical Statistics
publication_identifier:
  issn:
  - 1980-0436
publication_status: published
publisher: Instituto Nacional de Matematica Pura e Aplicada
quality_controlled: '1'
scopus_import: '1'
status: public
title: Transition to shocks in TASEP and decoupling of last passage times
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2018'
...
---
_id: '556'
abstract:
- lang: eng
  text: 'We investigate the free boundary Schur process, a variant of the Schur process
    introduced by Okounkov and Reshetikhin, where we allow the first and the last
    partitions to be arbitrary (instead of empty in the original setting). The pfaffian
    Schur process, previously studied by several authors, is recovered when just one
    of the boundary partitions is left free. We compute the correlation functions
    of the process in all generality via the free fermion formalism, which we extend
    with the thorough treatment of “free boundary states.” For the case of one free
    boundary, our approach yields a new proof that the process is pfaffian. For the
    case of two free boundaries, we find that the process is not pfaffian, but a closely
    related process is. We also study three different applications of the Schur process
    with one free boundary: fluctuations of symmetrized last passage percolation models,
    limit shapes and processes for symmetric plane partitions and for plane overpartitions.'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Dan
  full_name: Betea, Dan
  last_name: Betea
- first_name: Jeremie
  full_name: Bouttier, Jeremie
  last_name: Bouttier
- first_name: Peter
  full_name: Nejjar, Peter
  id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
  last_name: Nejjar
- first_name: Mirjana
  full_name: Vuletic, Mirjana
  last_name: Vuletic
citation:
  ama: Betea D, Bouttier J, Nejjar P, Vuletic M. The free boundary Schur process and
    applications I. <i>Annales Henri Poincare</i>. 2018;19(12):3663-3742. doi:<a href="https://doi.org/10.1007/s00023-018-0723-1">10.1007/s00023-018-0723-1</a>
  apa: Betea, D., Bouttier, J., Nejjar, P., &#38; Vuletic, M. (2018). The free boundary
    Schur process and applications I. <i>Annales Henri Poincare</i>. Springer Nature.
    <a href="https://doi.org/10.1007/s00023-018-0723-1">https://doi.org/10.1007/s00023-018-0723-1</a>
  chicago: Betea, Dan, Jeremie Bouttier, Peter Nejjar, and Mirjana Vuletic. “The Free
    Boundary Schur Process and Applications I.” <i>Annales Henri Poincare</i>. Springer
    Nature, 2018. <a href="https://doi.org/10.1007/s00023-018-0723-1">https://doi.org/10.1007/s00023-018-0723-1</a>.
  ieee: D. Betea, J. Bouttier, P. Nejjar, and M. Vuletic, “The free boundary Schur
    process and applications I,” <i>Annales Henri Poincare</i>, vol. 19, no. 12. Springer
    Nature, pp. 3663–3742, 2018.
  ista: Betea D, Bouttier J, Nejjar P, Vuletic M. 2018. The free boundary Schur process
    and applications I. Annales Henri Poincare. 19(12), 3663–3742.
  mla: Betea, Dan, et al. “The Free Boundary Schur Process and Applications I.” <i>Annales
    Henri Poincare</i>, vol. 19, no. 12, Springer Nature, 2018, pp. 3663–742, doi:<a
    href="https://doi.org/10.1007/s00023-018-0723-1">10.1007/s00023-018-0723-1</a>.
  short: D. Betea, J. Bouttier, P. Nejjar, M. Vuletic, Annales Henri Poincare 19 (2018)
    3663–3742.
date_created: 2018-12-11T11:47:09Z
date_published: 2018-11-13T00:00:00Z
date_updated: 2024-02-20T10:48:17Z
day: '13'
ddc:
- '500'
department:
- _id: LaEr
- _id: JaMa
doi: 10.1007/s00023-018-0723-1
ec_funded: 1
external_id:
  arxiv:
  - '1704.05809'
file:
- access_level: open_access
  checksum: 0c38abe73569b7166b7487ad5d23cc68
  content_type: application/pdf
  creator: dernst
  date_created: 2019-01-21T15:18:55Z
  date_updated: 2020-07-14T12:47:03Z
  file_id: '5866'
  file_name: 2018_Annales_Betea.pdf
  file_size: 3084674
  relation: main_file
file_date_updated: 2020-07-14T12:47:03Z
has_accepted_license: '1'
intvolume: '        19'
issue: '12'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 3663-3742
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
publication: Annales Henri Poincare
publication_identifier:
  issn:
  - 1424-0637
publication_status: published
publisher: Springer Nature
publist_id: '7258'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The free boundary Schur process and applications I
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 19
year: '2018'
...
---
_id: '447'
abstract:
- lang: eng
  text: We consider last passage percolation (LPP) models with exponentially distributed
    random variables, which are linked to the totally asymmetric simple exclusion
    process (TASEP). The competition interface for LPP was introduced and studied
    in Ferrari and Pimentel (2005a) for cases where the corresponding exclusion process
    had a rarefaction fan. Here we consider situations with a shock and determine
    the law of the fluctuations of the competition interface around its deter- ministic
    law of large number position. We also study the multipoint distribution of the
    LPP around the shock, extending our one-point result of Ferrari and Nejjar (2015).
article_processing_charge: No
article_type: original
author:
- first_name: Patrik
  full_name: Ferrari, Patrik
  last_name: Ferrari
- first_name: Peter
  full_name: Nejjar, Peter
  id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
  last_name: Nejjar
citation:
  ama: Ferrari P, Nejjar P. Fluctuations of the competition interface in presence
    of shocks. <i>Revista Latino-Americana de Probabilidade e Estatística</i>. 2017;9:299-325.
    doi:<a href="https://doi.org/10.30757/ALEA.v14-17">10.30757/ALEA.v14-17</a>
  apa: Ferrari, P., &#38; Nejjar, P. (2017). Fluctuations of the competition interface
    in presence of shocks. <i>Revista Latino-Americana de Probabilidade e Estatística</i>.
    Instituto Nacional de Matematica Pura e Aplicada. <a href="https://doi.org/10.30757/ALEA.v14-17">https://doi.org/10.30757/ALEA.v14-17</a>
  chicago: Ferrari, Patrik, and Peter Nejjar. “Fluctuations of the Competition Interface
    in Presence of Shocks.” <i>Revista Latino-Americana de Probabilidade e Estatística</i>.
    Instituto Nacional de Matematica Pura e Aplicada, 2017. <a href="https://doi.org/10.30757/ALEA.v14-17">https://doi.org/10.30757/ALEA.v14-17</a>.
  ieee: P. Ferrari and P. Nejjar, “Fluctuations of the competition interface in presence
    of shocks,” <i>Revista Latino-Americana de Probabilidade e Estatística</i>, vol.
    9. Instituto Nacional de Matematica Pura e Aplicada, pp. 299–325, 2017.
  ista: Ferrari P, Nejjar P. 2017. Fluctuations of the competition interface in presence
    of shocks. Revista Latino-Americana de Probabilidade e Estatística. 9, 299–325.
  mla: Ferrari, Patrik, and Peter Nejjar. “Fluctuations of the Competition Interface
    in Presence of Shocks.” <i>Revista Latino-Americana de Probabilidade e Estatística</i>,
    vol. 9, Instituto Nacional de Matematica Pura e Aplicada, 2017, pp. 299–325, doi:<a
    href="https://doi.org/10.30757/ALEA.v14-17">10.30757/ALEA.v14-17</a>.
  short: P. Ferrari, P. Nejjar, Revista Latino-Americana de Probabilidade e Estatística
    9 (2017) 299–325.
date_created: 2018-12-11T11:46:31Z
date_published: 2017-03-23T00:00:00Z
date_updated: 2023-10-10T13:10:32Z
day: '23'
department:
- _id: LaEr
- _id: JaMa
doi: 10.30757/ALEA.v14-17
ec_funded: 1
intvolume: '         9'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://alea.impa.br/articles/v14/14-17.pdf
month: '03'
oa: 1
oa_version: Submitted Version
page: 299 - 325
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Revista Latino-Americana de Probabilidade e Estatística
publication_status: published
publisher: Instituto Nacional de Matematica Pura e Aplicada
publist_id: '7376'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fluctuations of the competition interface in presence of shocks
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 9
year: '2017'
...