Related papers: A Spectral Approach to Kemeny's Constant
The recurrence features of persistent random walks built from variable length Markov chains are investigated. We observe that these stochastic processes can be seen as L{\'e}vy walks for which the persistence times depend on some internal…
As known, the commonly-utilized ways to determine mean first-passage time $\overline{\mathcal{F}}$ for random walk on networks are mainly based on Laplacian spectra. However, methods of this type can become prohibitively complicated and…
We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…
We suggest a non-asymptotic matrix perturbation-theoretic approach to get sharp bounds on the expected meeting time of random walks on large (possibly random) graphs. We provide a formula for the expected meeting time in terms of the…
We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to those predicted by suitable random matrix theory ensembles,…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
In this paper we develop a statistical estimation technique to recover the transition kernel $P$ of a Markov chain $X=(X_m)_{m \in \mathbb N}$ in presence of censored data. We consider the situation where only a sub-sequence of $X$ is…
We define the spectral gap of a Markov chain on a finite state space as the second-smallest singular value of the generator of the chain, generalizing the usual definition of spectral gap for reversible chains. We then define the relaxation…
We consider the continuous-time quantum walk defined on the adjacency matrix of a graph. At each instant, the walk defines a mixing matrix which is doubly-stochastic. The average of the mixing matrices contains relevant information about…
The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time…
For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the…
We use a random walk in the ensemble of impurity configurations to generate a Brownian motion model for energy levels in disordered conductors. Treating arc-length along the random walk as fictitous time, the resulting Langevin equation…
We define quantization scheme for discrete-time random walks on the half-line consistent with Szegedy's quantization of finite Markov chains. Motivated by the Karlin and McGregor description of discrete-time random walks in terms of…
We present a novel method for computing reachability probabilities of parametric discrete-time Markov chains whose transition probabilities are fractions of polynomials over a set of parameters. Our algorithm is based on two key…
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…
We introduce a general approach for the study of the collective dynamics of non-interacting random walkers on connected networks. We analyze the movement of $R$ independent (Markovian) walkers, each defined by its own transition matrix. By…
Random walks (or Markov chains) are models extensively used in theoretical computer science. Several tools, including analysis of quantities such as hitting and mixing times, are helpful for devising randomized algorithms. A notable example…
For a Markov chain $Y$ with values in a Polish space, consider the entrance Markov chain obtained by sampling $Y$ at the moments when it enters a fixed set $A$ from its complement $A^c$. Similarly, consider the exit Markov chain, obtained…
Various graph algorithms have been developed with multiple random walks, the movement of several independent random walkers on a graph. Designing an efficient graph algorithm based on multiple random walks requires investigating multiple…
This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…