相关论文: Cover times of the massive random walk loop soup

We consider the simple random walk conditioned to stay forever in a finite domain $D_N \subset \mathbb{Z}^d, d \geq 3$ of typical size $N$. This confined walk is a random walk on the conductances given by the first eigenvector of the…

We consider a continuous time random walk on the rooted binary tree of depth $n$ with all transition rates equal to one and study its cover time, namely the time until all vertices of the tree have been visited. We prove that, normalized by…

We consider a general random walk loop soup which includes, or is related to, several models of interest, such as the Spin O(N) model, the double dimer model and the Bose gas. The analysis of this model is challenging because of the…

Let R_n be the radius of the largest disk covered after n steps of a simple random walk. We prove that almost surely limsup_{n \to \infty}(log R_n)^2/(log n log_3 n) = 1/4, where log_3 denotes 3 iterations of the log function. This is…

We provide conditions that classify cover times for sequences of random walks on random graphs into two types: One type (Type 1) is the class of cover times that are of the order of the maximal hitting times scaled by the logarithm of the…

We study random walks on the giant component of Hyperbolic Random Graphs (HRGs), in the regime when the degree distribution obeys a power law with exponent in the range $(2,3)$. In particular, we first focus on the expected time for a…

In this article, we study a covering process of the discrete one-dimensional torus that uses connected arcs of random sizes in the covering. More precisely, fix a distribution \mu on \mathbb{N}, and for every n\geq 1 we will cover the torus…

In this paper we deal with the classical problem of random cover times. We investigate the distribution of the time it takes for a Poisson process of cylinders to cover a set $A \subset \mathbb{R}^d.$ This Poisson process of cylinders is…

Consider a sequence of Poisson point processes of non-trivial loops with certain intensity measures $(\mu^{(n)})_n$, where each $\mu^{(n)}$ is explicitly determined by transition probabilities $p^{(n)}$ of a random walk on a finite state…

We consider a random walk among a Poisson system of moving traps on ${\mathbb Z}$. In earlier work [DGRS12], the quenched and annealed survival probabilities of this random walk have been investigated. Here we study the path of the random…

We study the random sequential adsorption of $k$-mers on the fully-connected lattice with $N=kn$ sites. The probability distribution $T_n(s,t)$ of the time $t$ needed to cover the lattice with $s$ $k$-mers is obtained using a generating…

This work proves that the fluctuations of the cover time of simple random walk in the discrete torus of dimension at least three with large side-length are governed by the Gumbel extreme value distribution. This result was conjectured for…

Among observables characterising the random exploration of a graph or lattice, the cover time, namely the time to visit every site, continues to attract widespread interest. Much insight about cover times is gained by mapping to the…

The cover-time problem, i.e., time to visit every site in a system, is one of the key issues of random walks with wide applications in natural, social, and engineered systems. Addressing the full distribution of cover times for random walk…

We study a random walk that prefers tou se unvisited edges in the context of random cubic graphs. We establish asymptotically correct estimates for the vertex and edge cover times, these being $\approx n\log n$ and $\approx \frac32n\log n$…

We study the cover time $\tau_{\mathrm{cov}}$ by (continuous-time) random walk on the 2D box of side length $n$ with wired boundary or on the 2D torus, and show that in both cases with probability approaching 1 as $n$ increases,…

Let $T_n$ denote the binary tree of depth $n$ augmented by an extra edge connected to its root. Let $C_n$ denote the cover time of $T_n$ by simple random walk. We prove that $\sqrt{ \mathcal{C}_{n} 2^{-(n+1) } } - m_n$ converges in…

We present analytical results for the distribution of cover times of random walks (RWs) on random regular graphs consisting of $N$ nodes of degree $c$ ($c \ge 3$). Starting from a random initial node at time $t=1$, at each time step $t \ge…

We consider a random walk on the fully-connected lattice with $N$ sites and study the time evolution of the number of distinct sites $s$ visited by the walker on a subset with $n$ sites. A record value $v$ is obtained for $s$ at a record…

We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…