Cutoff on Ramanujan complexes and classical groups

Michael Chapman; Ori Parzanchevski

doi:https://doi.org/10.4171/CMH/537

Cutoff on Ramanujan complexes and classical groups

Michael Chapman, Ori Parzanchevski

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

The total-variation cutoff phenomenon has been conjectured to hold for simple random walk on all transitive expanders. However, very little is actually known regarding this conjecture, and cutoff on sparse graphs in general. In this paper we establish total-variation cutoff for simple random walk on Ramanujan complexes of type A^z_d (d 1). As a result, we obtain explicit generators for the finite classical groups PGL_n.F_q/ for which the associated Cayley graphs exhibit total-variation cutoff.

Original language	English
Pages (from-to)	431-456
Number of pages	26
Journal	Commentarii Mathematici Helvetici
Volume	97
Issue number	3
DOIs	https://doi.org/10.4171/CMH/537
State	Published - 2022

Keywords

Bruhat–Tits buildings
Cutoff
Ramanujan complexes
expanders
random walks

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

https://doi.org/10.4171/CMH/537

Cite this

@article{2c1350fd6bb44c3b84375563d6117dfd,

title = "Cutoff on Ramanujan complexes and classical groups",

abstract = "The total-variation cutoff phenomenon has been conjectured to hold for simple random walk on all transitive expanders. However, very little is actually known regarding this conjecture, and cutoff on sparse graphs in general. In this paper we establish total-variation cutoff for simple random walk on Ramanujan complexes of type Azd (d 1). As a result, we obtain explicit generators for the finite classical groups PGLn.Fq/ for which the associated Cayley graphs exhibit total-variation cutoff.",

keywords = "Bruhat–Tits buildings, Cutoff, Ramanujan complexes, expanders, random walks",

author = "Michael Chapman and Ori Parzanchevski",

year = "2022",

doi = "https://doi.org/10.4171/CMH/537",

language = "الإنجليزيّة",

volume = "97",

pages = "431--456",

journal = "Commentarii Mathematici Helvetici",

issn = "0010-2571",

publisher = "European Mathematical Society Publishing House",

number = "3",

}

TY - JOUR

T1 - Cutoff on Ramanujan complexes and classical groups

AU - Chapman, Michael

AU - Parzanchevski, Ori

PY - 2022

Y1 - 2022

N2 - The total-variation cutoff phenomenon has been conjectured to hold for simple random walk on all transitive expanders. However, very little is actually known regarding this conjecture, and cutoff on sparse graphs in general. In this paper we establish total-variation cutoff for simple random walk on Ramanujan complexes of type Azd (d 1). As a result, we obtain explicit generators for the finite classical groups PGLn.Fq/ for which the associated Cayley graphs exhibit total-variation cutoff.

AB - The total-variation cutoff phenomenon has been conjectured to hold for simple random walk on all transitive expanders. However, very little is actually known regarding this conjecture, and cutoff on sparse graphs in general. In this paper we establish total-variation cutoff for simple random walk on Ramanujan complexes of type Azd (d 1). As a result, we obtain explicit generators for the finite classical groups PGLn.Fq/ for which the associated Cayley graphs exhibit total-variation cutoff.

KW - Bruhat–Tits buildings

KW - Cutoff

KW - Ramanujan complexes

KW - expanders

KW - random walks

UR - http://www.scopus.com/inward/record.url?scp=85139828470&partnerID=8YFLogxK

U2 - https://doi.org/10.4171/CMH/537

DO - https://doi.org/10.4171/CMH/537

M3 - مقالة

SN - 0010-2571

VL - 97

SP - 431

EP - 456

JO - Commentarii Mathematici Helvetici

JF - Commentarii Mathematici Helvetici

IS - 3

ER -

Cutoff on Ramanujan complexes and classical groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this