Work

Mixing time of the lazy and simple random walk on a randomly twisted hypercube

Year: 2026

Type: preprint

Abstract: We consider a randomly twisted hypercube on $N$ vertices and study a simple or lazy random walk on this graph. We show that for both walks the mixing time is of order $\log N$, and the model does not exhibit cutoff. We also establish that both walks have cover time of order $N\log N$, and we show that the chromatic number of the graph diverges.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.21976

Authors: Baran, Zsuzsanna, Šarković, Anđela

Institutions: Université Paris Dauphine-PSL, University of Cambridge

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Engineering and Physical Sciences Research Council

OpenAlex ID: W7222509569

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