Related papers: Mixing Time for Some Adjacent Transposition Markov…
This paper deals with a complete bipartite matching problem with the objective of finding an optimal matching that maximizes a certain generic predefined utility function on the set of all matchings. After proving the NP-hardness of the…
We consider the irreducibility of switch-based Markov chains for the approximate uniform sampling of Hamiltonian cycles in a given undirected dense graph on $n$ vertices. As our main result, we show that every pair of Hamiltonian cycles in…
Markov chains are one of the well-known tools for modeling and analyzing stochastic systems. At the same time, they are used for constructing random walks that can achieve a given stationary distribution. This paper is concerned with…
A discrete-time Markov chain can be transformed into a new Markov chain by looking at its states along iterations of an almost surely finite stopping time. By the optional stopping theorem, any bounded harmonic function with respect to the…
The Poisson process of order $i$ is a weighted sum of independent Poisson processes and is used to model the flow of clients in different services. In the paper below we study some extensions of this process, for different forms of the…
We provide new upper bounds for mixing times of general finite Markov chains. We use these bounds to show that the total variation mixing time is robust under rough isometry for bounded degree graphs that are roughly isometric to trees.
Without mutation and migration, evolutionary dynamics ultimately leads to the extinction of all but one species. Such fixation processes are well understood and can be characterized analytically with methods from statistical physics.…
Mahlmann and Schindelhauer (2005) defined a Markov chain which they called $k$-Flipper, and showed that it is irreducible on the set of all connected regular graphs of a given degree (at least 3). We study the 1-Flipper chain, which we call…
We show a strict hierarchy among various edge and vertex expansion properties of Markov chains. This gives easy proofs of a range of bounds, both classical and new, on chi-square distance, spectral gap and mixing time. The 2-gradient is…
Consider a discrete time, ergodic Markov chain with finite state space which is started from stationarity. Fill and Lyzinski (2014) showed that, in some cases, the hitting time for a given state may be represented as a sum of a geometric…
Contingency tables are useful objects in statistics for representing 2-way data. With fixed row and column sums, and a total of $n$ entries, contingency tables correspond to parabolic double cosets of $S_n$. The uniform distribution on…
Consider the random walk on the permutation group obtained when the step distribution is uniform on a given conjugacy class. It is shown that there is a critical time at which two phase transitions occur simultaneously. On the one hand, the…
We show that a new probabilistic technique, recently introduced by the first author, yields the sharpest bounds obtained to date on mixing times of Markov chains in terms of isoperimetric properties of the state space (also known as…
We develop two models for Bayesian estimation and selection in high-order, discrete-state Markov chains. Both are based on the mixture transition distribution, which constructs a transition probability tensor with additive mixing of…
We propose a method to approximate continuous-time, continuous-state stochastic processes by a discrete-time Markov chain defined on a nonuniform grid. Our method provides exact moment matching for processes whose first and second moments…
There is a well-established theory linking certain semi-Markov chains and continuous-time random walks to time-fractional equations and anomalous diffusion. In this work, we go beyond the semi-Markov framework by considering some…
We introduce a variation of strong stationary times for random walks on the symmetric group. Rather than proceed in the usual fashion of accumulating larger and larger blocks of cards which may be in any order, we wait for pairs of cards to…
We establish upper and lower bounds on the maximal number of steps needed to transform a cyclic permutation to the canonical cyclic permutation using conjugation by adjacent transpositions, and on the diameter of the underlying Schreier…
The switch chain is a well-studied Markov chain which generates random graphs with a given degree sequence and has uniform stationary distribution. Motivated by the high number of triangles seen in some real-world networks, we study a…
We consider a simple discrete-time Markov chain with values in $[0,\infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary…