• Corpus ID: 244347165

A limit law for the most favorite point of simple random walk on a regular tree

  title={A limit law for the most favorite point of simple random walk on a regular tree},
  author={Marek Tomasz Biskup and Oren Louidor},
: We consider a continuous-time random walk on a regular tree of finite depth and study its favorite points among the leaf vertices. We prove that, for the walk started from a leaf vertex and stopped upon hitting the root, as the depth of the tree tends to infinity the maximal time spent at any leaf converges, under suitable scaling and centering, to a randomly-shifted Gumbel law. The random shift is characterized using a derivative-martingale like object associated with square-root local-time… 

Exceptional points of two-dimensional random walks at multiples of the cover time

We study exceptional sets of the local time of the continuous-time simple random walk in scaled-up (by $N$) versions $D_N\subset\mathbb Z^2$ of bounded open domains $D\subset\mathbb R^2$. Upon exit



A Scaling Limit for the Cover Time of the Binary Tree

Convergence in Law for the Branching Random Walk Seen from Its Tip

Consider a critical branching random walk on the real line. In a recent paper, Aïdékon (2011) developed a powerful method to obtain the convergence in law of its minimum after a log-factor

Maximum and minimum of local times for two-dimensional random walk

  • Y. Abe
  • Mathematics, Physics
  • 2014
We obtain the leading orders of the maximum and the minimum of local times for the simple random walk on the two-dimensional torus at time proportional to the cover time. We also estimate the number

Some problems concerning the structure of random walk paths

1. In t roduct ion . We restrict our consideration to symmetric random walk, defined in the following way. Consider the lattice formed by the points of d-dimensional Euclidean space whose coordinates

Convergence in law of the minimum of a branching random walk

We consider the minimum of a super-critical branching random walk. Addario-Berry and Reed [Ann. Probab. 37 (2009) 1044–1079] proved the tightness of the minimum centered around its mean value. We

Decorated Random Walk Restricted to Stay Below a Curve (Supplement Material)

We consider a one dimensional random-walk-like process, whose steps are centered Gaussians with variances which are determined according to the sequence of arrivals of a Poisson process on the line.

Convergence in law of the maximum of nonlattice branching random walk

Let $\eta^*_n$ denote the maximum, at time $n$, of a nonlattice one-dimensional branching random walk $\eta_n$ possessing (enough) exponential moments. In a seminal paper, Aidekon demonstrated

Thick points for planar Brownian motion and the Erdős-Taylor conjecture on random walk

and conjectured that the limit exists and equals 1/Tr a.s. The importance of determining the value of this limit is clarified in (1.3) below, where this value appears in the power laws governing the

The structure of extreme level sets in branching Brownian motion

We study the structure of extreme level sets of a standard one dimensional branching Brownian motion, namely the sets of particles whose height is within a fixed distance from the order of the global

Asymptotics of cover times via Gaussian free fields: Bounded-degree graphs and general trees

In this paper we show that on bounded degree graphs and general trees, the cover time of the simple random walk is asymptotically equal to the product of the number of edges and the square of the