This book is an introduction to the modern theory of Markov chains, whose goal is to
determine the rate of convergence to the stationary distribution, as a function of state space …

We consider the biased card shuffling and the Asymmetric Simple Exclusion Process
(ASEP) on the segment. We obtain the asymptotic of their mixing times: our results show that …

We study mixing times of the symmetric and asymmetric simple exclusion process on the
segment where particles are allowed to enter and exit at the endpoints. We consider …

This paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP)
on a segment of length N. Our main result is that for particle densities in (0, 1), the total …

Appendices B and C. In two further Appendices, we provide details on the ways to relax
some assumptions as discussed in Section 1.4 and give the technical proofs of Corollaries …

We consider the simple exclusion process with k particles on a segment of length N
performing random walks with transition p>1/2 to the right and q=1-p to the left. We focus on …

We consider the exclusion process on segments of the integers in a site-dependent random
environment. We assume to be in the ballistic regime in which a single particle has positive …

Monotonic surfaces spanning finite regions of ℤd arise in many contexts, including DNA-
based self-assembly, card-shuffling and lozenge tilings. One method that has been used to …

Graded posets frequently arise throughout combinatorics, where it is natural to try to count
the number of elements of a fixed rank. These counting problems are often# P-complete, so …

We investigate the mixing time of the asymmetric Zero Range process on the segment with a
non-decreasing rate. We show that the cutoff holds in the totally asymmetric case with a …