## Electronic Communications in Probability

- Electron. Commun. Probab.
- Volume 23 (2018), paper no. 32, 10 pp.

### Cutoff for a stratified random walk on the hypercube

Anna Ben-Hamou and Yuval Peres

#### Abstract

We consider the random walk on the hypercube which moves by picking an ordered pair $(i,j)$ of distinct coordinates uniformly at random and adding the bit at location $i$ to the bit at location $j$, modulo $2$. We show that this Markov chain has cutoff at time $\frac{3} {2}n\log n$ with window of size $n$, solving a question posed by Chung and Graham (1997).

#### Article information

**Source**

Electron. Commun. Probab., Volume 23 (2018), paper no. 32, 10 pp.

**Dates**

Received: 12 December 2017

Accepted: 10 April 2018

First available in Project Euclid: 26 May 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.ecp/1527300061

**Digital Object Identifier**

doi:10.1214/18-ECP132

**Mathematical Reviews number (MathSciNet)**

MR3812064

**Zentralblatt MATH identifier**

1397.60096

**Subjects**

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

**Keywords**

Markov chains mixing times cutoff hypercube

**Rights**

Creative Commons Attribution 4.0 International License.

#### Citation

Ben-Hamou, Anna; Peres, Yuval. Cutoff for a stratified random walk on the hypercube. Electron. Commun. Probab. 23 (2018), paper no. 32, 10 pp. doi:10.1214/18-ECP132. https://projecteuclid.org/euclid.ecp/1527300061