Related papers: Near-critical spanning forests and renormalization

Consider a sequence (indexed by n) of Markov chains Z^n in R^d characterized by transition kernels that approximately (in n) depend only on the rescaled state n^{-1} Z^n. Subject to a smoothness condition, such a family can be closely…

Extreme-value theory for random vectors and stochastic processes with continuous trajectories is usually formulated for random objects all of whose univariate marginal distributions are identical. In the spirit of Sklar's theorem from…

We consider a 2-dimensional model of random walk in random environment known as line model. The environment is described by two independent families of i.i.d. random variables dictating rates of jumps in vertical, respectively horizontal…

The methodology based on the random walk processes is adapted and applied to a comprehensive analysis of the statistical properties of the probability fluxes. To this aim we define a simple model of the Markovian stochastic dynamics on a…

We derive the Markov process equivalent to She-Leveque scaling in homogeneous and isotropic turbulence. The Markov process is a jump process for velocity increments $u(r)$ in scale $r$ in which the jumps occur randomly but with…

Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given `far away' observations. Several theoretical results (and simple algorithms) are available when…

Similarly as in (Blancas et al. 2018) where nested coalescent processes are studied, we generalize the definition of partition-valued homogeneous Markov fragmentation processes to the setting of nested partitions, i.e. pairs of partitions…

We prove a quantitative Russo-Seymour-Welsh (RSW) type result for random walks on two natural examples of random planar graphs: the supercritical percolation cluster in the square lattice and the Poisson Voronoi triangulation in the plane.…

We define some new sequences of recursively constructed random combinatorial trees, and show that, after properly rescaling graph distance and equipping the trees with the uniform measure on vertices, each sequence converges almost surely…

We design fast algorithms for repeatedly sampling from strongly Rayleigh distributions, which include random spanning tree distributions and determinantal point processes. For a graph $G=(V, E)$, we show how to approximately sample…

We establish inequalities for assessing the distance between the distribution of a (possibly multidimensional) functional of a Poisson random measure and that of a Gaussian element. Our bounds only involve add-one cost operators at the…

We study spanning diverging forests of a digraph and related matrices. It is shown that the normalized matrix of out forests of a digraph coincides with the transition matrix in a specific observation model for Markov chains related to the…

We study a Markovian model for the random fragmentation of an object. At each time, the state consists of a collection of blocks. Each block waits an exponential amount of time with parameter given by its size to some power $\alpha$,…

This paper considers linear functions constructed on two different weighted branching processes and provides explicit bounds for their Kantorovich-Rubinstein distance in terms of couplings of their corresponding generic branching vectors.…

Aldous, Evans and Pitman (1998) studied the behavior of the fragmentation process derived from deleting the edges of a uniform random tree on $n$ labelled vertices. In particular, they showed that, after proper rescaling, the above…

We find explicit formulas for the probabilities of general boundary visit events for planar loop-erased random walks, as well as connectivity events for branches in the uniform spanning tree. We show that both probabilities, when suitably…

In this article, we consider a Branching Random Walk on the real line. The genealogical structure is assumed to be given through a supercritical branching process in the i.i.d. environment and satisfies the Kesten-Stigum condition. The…

Understanding and predicting how complex systems respond to external perturbations is a central challenge in nonequilibrium statistical physics. Here we consider continuous-time Markov networks, which we subject to perturbations along a…

For $\alpha \in (1,2]$, the $\alpha$-stable graph arises as the universal scaling limit of critical random graphs with i.i.d. degrees having a given $\alpha$-dependent power-law tail behavior. It consists of a sequence of compact measured…

We present a new pruning procedure on discrete trees by adding marks on the nodes of trees. This procedure allows us to construct and study a tree-valued Markov process $\{{\cal G}(u)\}$ by pruning Galton-Watson trees and an analogous…