---
_id: '13145'
abstract:
- lang: eng
text: We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary
finite diffuse measure space. We provide an interpretation of this characterization
in analogy with the Mecke identity for Poisson point processes.
acknowledgement: Research supported by the Sfb 1060 The Mathematics of Emergent Effects
(University of Bonn). L.D.S. gratefully acknowledges funding of his current position
by the Austrian Science Fund (FWF) through project ESPRIT 208.
article_processing_charge: No
article_type: original
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Eugene
full_name: Lytvynov, Eugene
last_name: Lytvynov
citation:
ama: Dello Schiavo L, Lytvynov E. A Mecke-type characterization of the Dirichlet–Ferguson
measure. Electronic Communications in Probability. 2023;28:1-12. doi:10.1214/23-ECP528
apa: Dello Schiavo, L., & Lytvynov, E. (2023). A Mecke-type characterization
of the Dirichlet–Ferguson measure. Electronic Communications in Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/23-ECP528
chicago: Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization
of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability.
Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-ECP528.
ieee: L. Dello Schiavo and E. Lytvynov, “A Mecke-type characterization of the Dirichlet–Ferguson
measure,” Electronic Communications in Probability, vol. 28. Institute
of Mathematical Statistics, pp. 1–12, 2023.
ista: Dello Schiavo L, Lytvynov E. 2023. A Mecke-type characterization of the Dirichlet–Ferguson
measure. Electronic Communications in Probability. 28, 1–12.
mla: Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization
of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability,
vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–12, doi:10.1214/23-ECP528.
short: L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28
(2023) 1–12.
date_created: 2023-06-18T22:00:48Z
date_published: 2023-05-05T00:00:00Z
date_updated: 2023-12-13T11:24:57Z
day: '05'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1214/23-ECP528
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isi:
- '001042025400001'
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publisher: Institute of Mathematical Statistics
quality_controlled: '1'
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title: A Mecke-type characterization of the Dirichlet–Ferguson measure
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...
---
_id: '12104'
abstract:
- lang: eng
text: We study ergodic decompositions of Dirichlet spaces under intertwining via
unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular
Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore,
every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces
is decomposable over their ergodic decompositions up to conjugation via an isomorphism
of the corresponding indexing spaces.
acknowledgement: Research supported by the Austrian Science Fund (FWF) grant F65 at
the Institute of Science and Technology Austria and by the European Research Council
(ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully
acknowledges funding of his current position by the Austrian Science Fund (FWF)
through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding
of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme
(Grant No. 156).
article_number: '9'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order
isomorphisms. Journal of Evolution Equations. 2023;23(1). doi:10.1007/s00028-022-00859-7
apa: Dello Schiavo, L., & Wirth, M. (2023). Ergodic decompositions of Dirichlet
forms under order isomorphisms. Journal of Evolution Equations. Springer
Nature. https://doi.org/10.1007/s00028-022-00859-7
chicago: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of
Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations.
Springer Nature, 2023. https://doi.org/10.1007/s00028-022-00859-7.
ieee: L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms
under order isomorphisms,” Journal of Evolution Equations, vol. 23, no.
1. Springer Nature, 2023.
ista: Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms
under order isomorphisms. Journal of Evolution Equations. 23(1), 9.
mla: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet
Forms under Order Isomorphisms.” Journal of Evolution Equations, vol. 23,
no. 1, 9, Springer Nature, 2023, doi:10.1007/s00028-022-00859-7.
short: L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).
date_created: 2023-01-08T23:00:53Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2023-06-28T11:54:35Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00028-022-00859-7
ec_funded: 1
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- '000906214600004'
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file_size: 422612
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intvolume: ' 23'
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issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
- _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833
grant_number: ESP156_N
name: Gradient flow techniques for quantum Markov semigroups
publication: Journal of Evolution Equations
publication_identifier:
eissn:
- 1424-3202
issn:
- 1424-3199
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Ergodic decompositions of Dirichlet forms under order isomorphisms
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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)
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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...