Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A probabilistic proof of cutoff in the Metropolis algorithm for the
  Erd\H{o}s-R\'enyi random graph   We study mixing of the Metropolis algorithm for a distribution on the
hypercube that corresponds to the Erd\H{o}s-R\'enyi random graph with edge
probability p. This Markov chain has cutoff at max{p,1-p} n log n with window
size n, a result proved by Diaconis and Ram (2000) using Fourier analysis. Here
we give an alternative proof that relies on coupling and a projection to a
two-dimensional Markov chain. This is done in the hope that probabilistic
techniques will be easier to generalize to less symmetric distributions. We
also describe a close relationship between the Metropolis and Gibbs samplers
for this model. Our proof extends to the case where the edge probabilities vary
with n. In that case, we also show that a natural coordinate wise coupling is
sharp if and only if the edge probabilities are of order 1/n.

11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci