Dynamic random walks in Clifford algebras

被引：3

作者：

Schott, R. ^{[1
,2
]}

Staples, G. S. ^{[3
]}

机构：

[1] Univ Nancy 1, IECN, BP 239, F-54506 Vandoeuvre Les Nancy, France

[2] Univ Nancy 1, LORIA, F-54506 Vandoeuvre Les Nancy, France

[3] Southern Illinois Univ, Dept Math & Stat, Edwardsville, IL 62026 USA

来源：

ADVANCES IN PURE AND APPLIED MATHEMATICS | 2010年 / 1卷 / 01期

关键词：

Clifford algebras; random walks; dynamical systems; hypercubes;

D O I：

10.1515/APAM.2010.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a Clifford algebra of arbitrary signature Cl-p,Cl-q, p + q = n, multiplicative random walks with dynamic transitions are induced by sequences of random variables taking values in the unit basis vectors and paravectors of the algebra. These walks can be viewed as random walks on "directed hypercubes". Properties of such multiplicative walks are investigated, and these multiplicative walks are then summed to induce additive walks on the algebra. Properties of both types of walks are considered, and limit theorems are developed.

引用

页码：81 / 115

页数：35

共 50 条

[21] A generalized FFT for Clifford algebras [J].

Leopardi, P .

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2004, 11 (05) :663-688

[22] Cover time and mixing time of random walks on dynamic graphs [J].

Avin, Chen ;

Koucky, Michal ;

Lotker, Zvi .

RANDOM STRUCTURES & ALGORITHMS, 2018, 52 (04) :576-596

[23] Fast Distributed Computation in Dynamic Networks via Random Walks [J].

Das Sarma, Atish ;

Molla, Anisur Rahaman ;

Pandurangan, Gopal .

DISTRIBUTED COMPUTING, DISC 2012, 2012, 7611 :136-150

[24] RANDOM WALKS ON THE RANDOM GRAPH [J].

Berestycki, Nathanael ;

Lubetzky, Eyal ;

Peres, Yuval ;

Sly, Allan .

ANNALS OF PROBABILITY, 2018, 46 (01) :456-490

[25] How random are random walks? [J].

Blei, R .

SEMINAR ON STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS III, 2002, 52 :19-31

[26] Resource location based on precomputed partial random walks in dynamic networks [J].

Lopez Millan, Victor M. ;

Cholvi, Vicent ;

Fernandez Anta, Antonio ;

Lopez, Luis .

COMPUTER NETWORKS, 2016, 103 :165-180

[27] Continuity and Anomalous Fluctuations in Random Walks in Dynamic Random Environments: Numerics, Phase Diagrams and Conjectures [J].

L. Avena ;

P. Thomann .

Journal of Statistical Physics, 2012, 147 :1041-1067

[28] Law of large numbers for ballistic random walks in dynamic random environments under lateral decoupling [J].

Arcanjo, Weberson S. ;

Baldasso, Rangel ;

Hilario, Marcelo R. ;

dos Santos, Renato S. .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2025, 61 (02) :822-849

[29] Continuity and Anomalous Fluctuations in Random Walks in Dynamic Random Environments: Numerics, Phase Diagrams and Conjectures [J].

Avena, L. ;

Thomann, P. .

JOURNAL OF STATISTICAL PHYSICS, 2012, 147 (06) :1041-1067

[30] Vector coherent states on Clifford algebras [J].

K. Thirulogasanthar ;

A. L. Hohouéto .

Theoretical and Mathematical Physics, 2005, 143 :494-504

← 1 2 3 4 5 →