相关论文: Rapid mixing of the down-up walk on matchings of a…

Let $G$ be a graph with no isolated vertex. A matching in $G$ is a set of edges that are pairwise not adjacent in $G$, while the matching number, $\alpha'(G)$, of $G$ is the maximum size of a matching in $G$. The path covering number,…

Search patterns of randomly oriented steps of different lengths have been observed on all scales of the biological world, ranging from the microscopic to the ecological, including in protein motors, bacteria, T-cells, honeybees, marine…

Given a finite graph G, a vertex of the lamplighter graph consists of a zero-one labeling of the vertices of G, and a marked vertex of G. For transitive graphs G, we show that, up to constants, the relaxation time for simple random walk in…

We characterize the extremal structures for mixing walks on trees that start from the most advantageous vertex. Let $G=(V,E)$ be a tree with stationary distribution $\pi$. For a vertex $v \in V$, let $H(v,\pi)$ denote the expected length of…

We study a variant of the down-up and up-down walks over an $n$-partite simplicial complex, which we call expanderized higher order random walks -- where the sequence of updated coordinates correspond to the sequence of vertices visited by…

We prove that the well-studied triangulation flip walk on a convex point set mixes in time O(n^3 log^3 n), the first progress since McShine and Tetali's O(n^5 log n) bound in 1997. In the process we give lower and upper bounds of…

We study the mixing time of the Dikin walk in a polytope - a random walk based on the log-barrier from the interior point method literature. This walk, and a close variant, were studied by Narayanan (2016) and Kannan-Narayanan (2012).…

A matching $M$ in a graph $G$ is acyclic if the subgraph of $G$ induced by the set of vertices that are incident to an edge in $M$ is a forest. We prove that every graph with $n$ vertices, maximum degree at most $\Delta$, and no isolated…

Mixing of finite time-homogeneous Markov chains is well understood nowadays, with a rich set of techniques to estimate their mixing time. In this paper, we study the mixing time of random walks in dynamic random environments. To that end,…

The mixing time of a random walk, with or without backtracking, on a random graph generated according to the configuration model on $n$ vertices, is known to be of order $\log n$. In this paper we investigate what happens when the random…

It is well known that the spectral gap of the down-up walk over an $n$-partite simplicial complex (also known as Glauber dynamics) cannot be better than $O(1/n)$ due to natural obstructions such as coboundaries. We study an alternative…

We prove that the the mixing time of the Glauber dynamics for sampling independent sets on $n$-vertex $k$-uniform hypergraphs is $O(n\log n)$ when the maximum degree $\Delta$ satisfies $\Delta \leq c 2^{k/2}$, improving on the previous…

We establish conditions on sequences of graphs which ensure that the mixing times of the random walks on the graphs in the sequence converge. The main assumption is that the graphs, associated measures and heat kernels converge in a…

Let $G_S$ be a graph with loops attached at each vertex in $S \subseteq V(G).$ In this article, we develop exact formulae for the number of closed $3$- and $4$-walks on $G_S$ in terms of vertex degrees and certain elementary subgraphs of…

A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…

Several inequalities are proved for the mixing time of discrete-time quantum walks on finite graphs. The mixing time is defined differently than in Aharonov, Ambainis, Kempe and Vazirani (2001) and it is found that for particular examples…

We introduce a Markov chain for sampling from the uniform distribution on a Riemannian manifold $\mathcal{M}$, which we call the $\textit{geodesic walk}$. We prove that the mixing time of this walk on any manifold with positive sectional…

An unweighted, undirected graph $G$ on $n$ nodes is said to have \emph{bandwidth} at most $k$ if its nodes can be labelled from $0$ to $n - 1$ such that no two adjacent nodes have labels that differ by more than $k$. It is known that one…

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 introduce a new technique for bounding the cover time of random walks by relating it to the runtime of randomized broadcast. In particular, we strongly confirm for dense graphs the intuition of Chandra et al. \cite{CRRST97} that "the…