Related papers: Coupling for features of random walks
We generalize the optimal coupling theorem to multiple random variables: Given a collection of random variables, it is possible to couple all of them so that any two differ with probability comparable to the total-variation distance between…
Markov models have been widely utilized for modelling user web navigation behaviour. In this work we propose a dynamic clustering-based method to increase a Markov model's accuracy in representing a collection of user web navigation…
The reciprocal class of a Markov path measure is the set of all mixtures of its bridges. We give characterizations of the reciprocal class of a continuous-time Markov random walk on a graph. Our main result is in terms of some reciprocal…
Using the electric and coupling approaches, we derive a series of results concerning the mixing times for the stratified random walk on the d-cube, inspired in the results of Chung and Graham (1997) Stratified random walks on the n-cube.
A mixing Markov chain is proved to be realized as a random walk in a directed graph subject to a synchronizing road coloring. The result ensures existence of appropriate random mappings in Propp--Wilson's coupling from the past. The proof…
We study the mixing time of the Rook's Walk Markov chain on a $d$-dimensional chess board of side length $n\geq 3$, where a rook moves by first selecting an axis uniformly at random and then selecting a new position along that axis…
Let 0<\alpha<1/2. We show that the mixing time of a continuous-time reversible Markov chain on a finite state space is about as large as the largest expected hitting time of a subset of stationary measure at least \alpha of the state space.…
We study the Markov chain on $\mathbf{F}_p$ obtained by applying a function $f$ and adding $\pm\gamma$ with equal probability. When $f$ is a linear function, this is the well-studied Chung--Diaconis--Graham process. We consider two cases:…
Motivated by applications of distributed linear estimation, distributed control and distributed optimization, we consider the question of designing linear iterative algorithms for computing the average of numbers in a network. Specifically,…
We study the relaxation time in the random walk with jumps. The random walk with jumps combines random walk based sampling with uniform node sampling and improves the performance of network analysis and learning tasks. We derive various…
A classical statistical inequality is used to show that the distance covariance of two bounded random vectors is bounded from above by a simple function of the dimensionality and the bounds of the random vectors. Two special cases that…
We introduce and study systems of randomly coupled maps (RCM) where the relevant parameter is the degree of connectivity in the system. Global (almost-) synchronized states are found (equivalent to the synchronization observed in globally…
In this work, we study how to efficiently obtain perfect samples from a discrete distribution $\mathcal{D}$ given access only to pairwise comparisons of elements of its support. Specifically, we assume access to samples $(x, S)$, where $S$…
We consider a system of particles which interact through a jump process. The jump intensities are functions of the proximity rank of the particles, a type of interaction referred to as topological in the literature. Such interactions have…
The mixing time of a graph is an important metric, which is not only useful in analyzing connectivity and expansion properties of the network, but also serves as a key parameter in designing efficient algorithms. We present an efficient…
Using coupling techniques based on Stein's method for probability approximation, we revisit classical variance bounding inequalities of Chernoff, Cacoullos, Chen and Klaassen. Taking advantage of modern coupling techniques allows us to…
We discuss a Monte Carlo Markov Chain (MCMC) procedure for the random sampling of some one-dimensional lattice paths with constraints, for various constraints. We show that an approach inspired by optimal transport allows us to bound…
We present a general approach to study the flooding time (a measure of how fast information spreads) in dynamic graphs (graphs whose topology changes with time according to a random process). We consider arbitrary converging Markovian…
Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are…
We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…