Related papers: Disconnection, random walks, and random interlacem…
Random transvections generate a walk on the space of symplectic forms on $\mathbf{F}_q^{2n}$. The main result is establishing cutoff for this Markov chain. After $n+c$ steps, the walk is close to uniform while before $n-c$, it is far from…
Consider the random set composed of particles initially distributed on Zd, d >= 2, according to a Poisson point process of intensity u > 0 and moving as independent simple symmetric random walks, the trap particles. We are interested in the…
In this paper we obtain a decoupling feature of the random interlacements process $\mathcal{I}^u \subset \mathbb{Z}^d$, at level $u$, $d\geq 3$. More precisely, we show that the trace of the random interlacements process on two disjoint…
We study downward deviations of the maximum local time of the discrete-time simple random walk on $\mathbb{Z}^d$, $d\ge 3$. In our previous paper \cite{li2026ldmaxlocal}, the corresponding upper bound was established, while the matching…
We consider connectivity properties of the Branching Interlacements model in $\mathbb{Z}^d,~d\ge5$, recently introduced by Angel, R\'ath and Zhu in 2016. Using stochastic dimension techniques we show that every two vertices visited by the…
We study the asymptotic behavior the exit times of random walk from Euclidean balls around the origin of the incipient infinite cluster in a manner inspired by [26]. We do this by obtaining bounds on the effective resistance between the…
We consider the branching capacity of the range of a simple random walk on $\mathbb Z^d$, with $d \ge 5$, and show that it falls in the same universality class as the volume and the capacity of the range of simple random walks and branching…
How does removal of sites by a random walk lead to blockage of percolation? To study this problem of correlated site percolation, we consider a random walk (RW) of $N=uL^d$ steps on a $d$-dimensional hypercubic lattice of size $L^d$ (with…
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 study the random walk $X$ on the range of a simple random walk on $\mathbb{Z}^d$ in dimensions $d\geq 4$. When $d\geq 5$ we establish quenched and annealed scaling limits for the process $X$, which show that the intersections of the…
An upper bound for the critical probability of long range bond percolation in $d=2$ and $d=3$ is obtained by connecting the bond percolation with the SIR epidemic model, thus complementing the lower bound result in Frei and Perkins…
For a multivariate random walk with i.i.d. jumps satisfying the Cramer moment condition and having a mean vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the positive orthant…
We introduce a new self-interacting random walk on the integers in a dynamic random environment and show that it converges to a pure diffusion in the scaling limit. We also find a lower bound on the diffusion coefficient in some special…
We study limit laws for simple random walks on supercritical long-range percolation clusters on the integer lattice. For the long range percolation model, the probability that two vertices are connected behaves asymptotically as a negative…
We consider random walks on $\Z^8$ indexed by the infinite invariant tree, which consists of an infinite spine and finite random trees attached to it on both sides. We establish the precise order of the non-intersection probability between…
We prove a conditional decoupling inequality for the model of random interlacements in dimension $d\geq 3$: the conditional law of random interlacements on a box (or a ball) $A_1$ given the (not very "bad") configuration on a "distant" set…
We show that a coupling of non-colliding simple random walkers on the complete graph on $n$ vertices can include at most $n - \log n$ walkers. This improves the only previously known upper bound of $n-2$ due to Angel, Holroyd, Martin,…
We consider a discrete time simple symmetric random walk among Bernoulli obstacles on $\mathbb{Z}^d$, $d\geq 2$, where the walk is killed when it hits an obstacle. It is known that conditioned on survival up to time $N$, the random walk…
The random interlacements $\mathscr{I}(u)$ at level $u$ has been introduced by Sznitman, as a Poissonian collection of independent simple random walk trajectories on $\mathbb{Z}^d$, $d\geq 3$, with intensity $u>0$. Since then, several works…
We consider the interlacement Poisson point process on the space of doubly-infinite Z^d-valued trajectories modulo time-shift, tending to infinity at positive and negative infinite times. The set of vertices and edges visited by at least…