马尔可夫性和汤普森群F

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-04-07 DOI:10.3842/SIGMA.2022.083

Claus Kostler, Arundhathi Krishnan

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引用次数: 3

摘要

我们证明了Thompson群F在非对易概率空间的自同构中的表示产生了一大类双边平稳非对易Markov过程。作为部分逆，张量扩张形式的双边平稳马尔可夫过程产生了F的表示。作为一个应用，并在Kümmerer的结果的基础上，我们将F的表示与经典概率中的双边平稳Markov过程经典地关联起来。

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Markovianity and the Thompson Group F

We show that representations of the Thompson group F in the automorphisms of a noncommutative probability space yield a large class of bilateral stationary noncommutative Markov processes. As a partial converse, bilateral stationary Markov processes in tensor dilation form yield representations of F. As an application, and building on a result of Kümmerer, we canonically associate a representation of F to a bilateral stationary Markov process in classical probability.

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.