Related papers: Infinite collision property for the three-dimensio…
A mated-CRT map is a random planar map obtained as a discretized mating of correlated continuum random trees. Mated-CRT maps provide a coarse-grained approximation of many other natural random planar map models (e.g., uniform triangulations…
We give a sufficient condition for the existence of the harmonic measure from infinity of transient random walks on weighted graphs. In particular, this condition is verified by the random conductance model on $\Z^d$, $d\geq 3$, when the…
We study three mixing properties of a graph: large algebraic connectivity, large Cheeger constant (isoperimetric number) and large spectral gap from 1 for the second largest eigenvalue of the transition probability matrix of the random walk…
This article is one of a triptych composed with [Che25a] and [Che25b], that aims at proving an asymptotic expansion to any order of the passage probability of an irreducible equivariant finite range random walk on a tree. In this text we…
The simple random walk on $\mathbb{Z}^p$ shows two drastically different behaviours depending on the value of $p$: it is recurrent when $p\in\{1,2\}$ while it escapes (with a rate increasing with $p$) as soon as $p\geq3$. This classical…
It is a celebrated fact that a simple random walk on an infinite $k$-ary tree for $k \geq 2$ returns to the initial vertex at most finitely many times during infinitely many transitions; it is called transient. This work points out the fact…
We study a simple random walk on an n-dimensional hypercube. For any starting position we find the probability of hitting vertex a before hitting vertex b, whenever a and b share the same edge. This generalizes the model in Doyle, P., and…
We study existence of percolation in the hierarchical group of order $N$, which is an ultrametric space, and transience and recurrence of random walks on the percolation clusters. The connection probability on the hierarchical group for two…
We prove an invariance principle for the bridge of a random walk conditioned to stay positive, when the random walk is in the domain of attraction of a stable law, both in the discrete and in the absolutely continuous setting. This includes…
In arXiv:1609.05666v1 [math.PR] a functional limit theorem was proved. It states that symmetric processes associated with resistance metric measure spaces converge when the underlying spaces converge with respect to the…
We study random walk among random conductance (RWRC) on complete graphs with N vertices. The conductances are i.i.d. and the sum of conductances emanating from a single vertex asymptotically has an infinitely divisible distribution…
We study the properties of random walks on complex trees. We observe that the absence of loops reflects in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and…
We define a random walk of a particle in $\mathbb{R}^3$ where the space is rotating. The particle is not glued to the space and will collide with it at random times, resulting in changes in its velocity and direction. After many collisions,…
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.…
In this article it is shown that the Brownian motion on the continuum random tree is the scaling limit of the simple random walks on any family of discrete $n$-vertex ordered graph trees whose search-depth functions converge to the Brownian…
We study graph-theoretic properties of the trace of a random walk on a random graph. We show that for any $\varepsilon>0$ there exists $C>1$ such that the trace of the simple random walk of length $(1+\varepsilon)n\ln{n}$ on the random…
We introduce a technique using nonbacktracking random walk for estimating the spectral radius of simple random walk. This technique relates the density of nontrivial cycles in simple random walk to that in nonbacktracking random walk. We…
We consider $d$ independent walkers in the same random environment in $\mathbb{Z}$. Our assumption on the law of the environment is such that a single walker is transient to the right but subballistic. We show that - no matter what $d$ is -…
Given a finite-range random walk on a finitely generated free group , what is the asymptotic behaviour, as the number of steps goes to infinity, of the sequence of probabilities that the random walk is at a given element of the group? In…
In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These…