Related papers: Cutoff for random walks on graphs with bottlenecks
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…
This paper explores the mixing time of the random transposition walk on permutations with one-sided interval restrictions. In particular, we're interested in the notion of cutoff, a phenomenon which occurs when mixing occurs in a window of…
The cutoff phenomenon for an ergodic Markov chain describes a sharp transition in the convergence to its stationary distribution, over a negligible period of time, known as cutoff window. We study the cutoff phenomenon for simple random…
We evaluate the mixing time of certain random walks on large unitary groups
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…
A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…
We use the correlation matrix of the generating distribution to determine the mixing time for random walks on the torus $(\mathbb{Z}/q\mathbb{Z})^n$. We present our method in the context of the Diaconis-Gangolli random walk on both the $1…
We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we…
Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…
This paper studies the on- and off-diagonal upper estimate and the two-sided transition probability estimate of random walks on weighted graphs.
Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…
We consider the averaging process on a graph, that is the evolution of a mass distribution undergoing repeated averages along the edges of the graph at the arrival times of independent Poisson processes. We establish cutoff phenomena for…
We prove a general theorem on cutoffs for symmetric exclusion and interchange processes on finite graphs $G_N=(V_N,E_N)$, under the assumption that either the graphs converge geometrically and spectrally to a compact metric measure space,…
Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the…
We investigate the mixing properties of a model of reversible Markov chains in random environment, which notably contains the simple random walk on the superposition of a deterministic graph and a second graph whose vertex set has been…
In this note, we demonstrate an instance of bounded-degree graphs of size $n$, for which the total variation mixing time for the random walk is decreased by a factor of $\log n/ \log\log n$ if we multiply the edge-conductances by bounded…
We explore the use of machine-learning techniques to detect quantum speedup in random walks on graphs. Specifically, we investigate the performance of three different neural-network architectures (variations on fully connected and…
Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an…
We consider a variant of the configuration model with an embedded community structure and study the mixing properties of a simple random walk on it. Every vertex has an internal $\mathrm{deg}^{\text{int}}\geq 3$ and an outgoing…
We consider the zero-range process with arbitrary bounded monotone rates on the complete graph, in the regime where the number of sites diverges while the density of particles per site converges. We determine the asymptotics of the mixing…