Commutative Monoid Duality

被引：1

作者：

Latz, Jan Niklas ^{[1
]}

Swart, Jan M. ^{[1
]}

机构：

[1] Czech Acad Sci, Inst Informat Theory & Automat, Pod Vodarenskou Vezi 4, Prague 18200 8, Czech Republic

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2023年 / 36卷 / 02期

关键词：

Interacting particle system; Duality; Monoid; Semiring; Primary; Secondary; MONOTONE;

D O I：

10.1007/s10959-022-01197-7

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We introduce two partially overlapping classes of pathwise dualities between interacting particle systems that are based on commutative monoids (semigroups with a neutral element) and semirings, respectively. For interacting particle systems whose local state space has two elements, this approach yields a unified treatment of the well-known additive and cancellative dualities. For local state spaces with three or more elements, we discover several new dualities.

引用

页码：1088 / 1115

页数：28

共 19 条

[1] ANNIHILATING BRANCHING-PROCESSES [J].

BRAMSON, M ;

DING, WD ;

DURRETT, R .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1991, 37 (01) :1-17

[2] Dualities in population genetics: A fresh look with new dualities [J].

Carinci, Gioia ;

Giardina, Cristian ;

Giberti, Claudio ;

Redig, Frank .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2015, 125 (03) :941-969

[3] A SAMPLE PATH PROOF OF THE DUALITY FOR STOCHASTICALLY MONOTONE MARKOV-PROCESSES [J].

CLIFFORD, P ;

SUDBURY, A .

ANNALS OF PROBABILITY, 1985, 13 (02) :558-565

[4]

Cox J.T., 1991, Random Walks, Brownian Motion, and Interacting Particle Systems: A Festschrift in Honor of Frank Spitzer, chapter Nonlinear Voter Models, P189

[5]

Forsythe G., 1955, P AM MATH SOC, V6, P443, DOI DOI 10.2307/2032786

[6] Duality and Hidden Symmetries in Interacting Particle Systems [J].

Giardina, Cristian ;

Kurchan, Jorge ;

Redig, Frank ;

Vafayi, Kiamars .

JOURNAL OF STATISTICAL PHYSICS, 2009, 135 (01) :25-55

[7]

Griffeath D., 1979, Lecture Notes in Mathematics, V714

[8]

Handjani SJ, 1999, ANN PROBAB, V27, P226

[9] On the notion(s) of duality for Markov processes [J].

Jansen, Sabine ;

Kurt, Noemi .

PROBABILITY SURVEYS, 2014, 11 :59-120

[10]

Krone SM, 1999, ANN APPL PROBAB, V9, P331

← 1 2 →