Related papers: Random motion on finite rings, I: commutative ring…

Here, a new two-dimensional process, discrete in time and space, that yields the results of both a random walk and a quantum random walk, is introduced. This model describes the population distribution of four coin states |1>,-|1>, |0> -|0>…

Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…

A Markov chain is considered whose states are orderings of an underlying fixed tree and whose transitions are local "random-to-front" reorderings, driven by a probability distribution on subsets of the leaves. The eigenvalues of the…

We provide a general framework for computing upper bounds on mixing times of finite Markov chains when its minimal ideal is left zero. Our analysis is based on combining results by Brown and Diaconis with our previous work on stationary…

We present a recurrence-transience classification for discrete-time Markov chains on manifolds with negative curvature. Our classification depends only on geometric quantities associated to the increments of the chain, defined via the…

We develop a general theory for Markov chains whose transition probabilities are the coefficients of descent operators on combinatorial Hopf algebras. These model the breaking-then-recombining of combinational objects. Examples include the…

A sequence of real numbers (x_n) is Benford if the significands, i.e. the fraction parts in the floating-point representation of (x_n) are distributed logarithmically. Similarly, a discrete-time irreducible and aperiodic finite-state Markov…

We obtain universal estimates on the convergence to equilibrium and the times of coupling for continuous time irreducible reversible finite-state Markov chains, both in the total variation and in the L^2 norms. The estimates in total…

Many seemingly disparate Markov chains are unified when viewed as random walks on the set of chambers of a hyperplane arrangement. These include the Tsetlin library of theoretical computer science and various shuffling schemes. If only…

The analysis of many problems of interest associated with Markov chains, e.g. stationary distributions, moments of first passage time distributions and moments of occupation time random variables, involves the solution of a system of linear…

The preparation of the stationary distribution of irreducible, time-reversible Markov chains is a fundamental building block in many heuristic approaches to algorithmically hard problems. It has been conjectured that quantum analogs of…

We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra.…

We consider continuous-space, discrete-time Markov chains on $\mathbb{R}^d$, that admit a finite number $N$ of metastable states. Our main motivation for investigating these processes is to analyse random Poincar\'e maps, which describe…

Markov chains are used to give a purely probabilistic way of understanding the conjugacy classes of the finite symplectic and orthogonal groups in odd characteristic. As a corollary of these methods one obtains a probabilistic proof of…

We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…

We consider pairwise Markov random fields which have a number of important applications in statistical physics, image processing and machine learning such as Ising model and labeling problem to name a couple. Our own motivation comes from…

Necessary and sufficient conditions for a Markov chain to be ergodic are that the chain is irreducible and aperiodic. This result is manifest in the case of random walks on finite groups by a statement about the support of the driving…

Considering a Markov chain defined on a cycle, near-quadratic improvement of mixing is shown when only a subtle perturbation is introduced to the structure and non-reversible transition probabilities are used. More precisely, a mixing time…

Let $R$ be a commutative ring with identity. A unit $u$ of $R$ is called exceptional if $1-u$ is also a unit. When $R$ is a finite commutative ring, we determine the additive and multiplicative structures of its exceptional units; and then…

We show that the convergence of finite state space Markov chains to stationarity can often be considerably speeded up by alternating every step of the chain with a deterministic move. Under fairly general conditions, we show that not only…