On extremal measures for conservative particle systems

Sunder Sethuraman

doi:10.1016/S0246-0203(00)01062-1

On extremal measures for conservative particle systems

Sunder Sethuraman

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

It is well known that the exclusion, zero-range and misanthrope particle systems possess families of invariant measures due to the mass conservation property. Although these families have been classified a great deal, a full characterization of their extreme points is not available. In this article, we consider an approach to the study of this classification. One of the results in this note is that the zero-range product invariant measures, ∏_i∈Sμ_α(·), for an infinite countable set S, under mild conditions, are identified as extremal for α(·)∈H_ZR where μ_α(i)(k)=Z(α(i))^-1α(i) ^k/g(1)g(k) with g and Z the rate function and normalization respectively, and H_ZR is the set of invariant measures for the transition probability p.

Original language	English (US)
Pages (from-to)	139-154
Number of pages	16
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	37
Issue number	2
DOIs	https://doi.org/10.1016/S0246-0203(00)01062-1
State	Published - Mar 2001

Keywords

Dirichlet form
Extreme points
Invariant measures
Misanthrope process
Primary 60K35
Secondary 60F05
Simple exclusion process
Zero-range process

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/S0246-0203(00)01062-1

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title = "On extremal measures for conservative particle systems",

abstract = "It is well known that the exclusion, zero-range and misanthrope particle systems possess families of invariant measures due to the mass conservation property. Although these families have been classified a great deal, a full characterization of their extreme points is not available. In this article, we consider an approach to the study of this classification. One of the results in this note is that the zero-range product invariant measures, ∏i∈Sμα(·), for an infinite countable set S, under mild conditions, are identified as extremal for α(·)∈HZR where μα(i)(k)=Z(α(i))-1α(i) k/g(1)g(k) with g and Z the rate function and normalization respectively, and HZR is the set of invariant measures for the transition probability p.",

keywords = "Dirichlet form, Extreme points, Invariant measures, Misanthrope process, Primary 60K35, Secondary 60F05, Simple exclusion process, Zero-range process",

author = "Sunder Sethuraman",

note = "Funding Information: ✩Research supported in part by NSF grant NSF/DMS-9703811. E-mail address: sethuram@iastate.edu (S. Sethuraman).",

year = "2001",

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doi = "10.1016/S0246-0203(00)01062-1",

language = "English (US)",

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T1 - On extremal measures for conservative particle systems

AU - Sethuraman, Sunder

N1 - Funding Information: ✩Research supported in part by NSF grant NSF/DMS-9703811. E-mail address: sethuram@iastate.edu (S. Sethuraman).

PY - 2001/3

Y1 - 2001/3

N2 - It is well known that the exclusion, zero-range and misanthrope particle systems possess families of invariant measures due to the mass conservation property. Although these families have been classified a great deal, a full characterization of their extreme points is not available. In this article, we consider an approach to the study of this classification. One of the results in this note is that the zero-range product invariant measures, ∏i∈Sμα(·), for an infinite countable set S, under mild conditions, are identified as extremal for α(·)∈HZR where μα(i)(k)=Z(α(i))-1α(i) k/g(1)g(k) with g and Z the rate function and normalization respectively, and HZR is the set of invariant measures for the transition probability p.

AB - It is well known that the exclusion, zero-range and misanthrope particle systems possess families of invariant measures due to the mass conservation property. Although these families have been classified a great deal, a full characterization of their extreme points is not available. In this article, we consider an approach to the study of this classification. One of the results in this note is that the zero-range product invariant measures, ∏i∈Sμα(·), for an infinite countable set S, under mild conditions, are identified as extremal for α(·)∈HZR where μα(i)(k)=Z(α(i))-1α(i) k/g(1)g(k) with g and Z the rate function and normalization respectively, and HZR is the set of invariant measures for the transition probability p.

KW - Dirichlet form

KW - Extreme points

KW - Invariant measures

KW - Misanthrope process

KW - Primary 60K35

KW - Secondary 60F05

KW - Simple exclusion process

KW - Zero-range process

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U2 - 10.1016/S0246-0203(00)01062-1

DO - 10.1016/S0246-0203(00)01062-1

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JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 2

ER -

On extremal measures for conservative particle systems

Abstract

Keywords

ASJC Scopus subject areas

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