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 present a novel method for reducing the computational complexity of rigorously
estimating the partition functions of Gibbs (or Boltzmann) distributions, which arise …

We introduce a novel statistical measure for MCMC-mean estimation, the inter-trace
variance ${\rm trv}^{(\tau_ {rel})}({\cal M}, f) $, which depends on a Markov chain ${\cal M} …

We study very simple sorting algorithms based on a probabilistic comparator model. In this
model, errors in comparing two elements are due to (1) the energy or effort put in the …

In this paper, we study a biased version of the nearest-neighbor transposition Markov chain
on the set of permutations where neighboring elements i and j are placed in order (i, j) with …

We study the mixing time of a Markov chain on biased permutations, a problem related to
self‐organizing lists. We are given probabilities pi, j,\left {p _ i, j\right\}, for all i≠ j, i ≠ j, such …

The spectral gap of a Markov chain can be bounded by the spectral gaps of constituent"
restriction" chains and a" projection" chain, and the strength of such a bound is the content of …

Algorithmic Problems Arising in Posets and Permutations Page 1 Algorithmic Problems Arising
in Posets and Permutations A Thesis Submitted to the Faculty in partial fulfillment of the …

In this paper, we study a biased version of the nearest-neighbor transposition Markov chain
on the set of permutations where neighboring elements and are placed in order with …

We prove rapid mixing for certain Markov chains on the set $ S_n $ of permutations on $1,
2,\dots, n $ in which adjacent transpositions are made with probabilities that depend on the …