Related papers: Near-critical spanning forests and renormalization
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
Another facet of the elegant link between random processes on graphs and Laplacian-based numerical linear algebra is uncovered: based on random spanning forests, novel Monte-Carlo estimators for graph signal smoothing are proposed. These…
Markov random fields are used to model high dimensional distributions in a number of applied areas. Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random…
We present a uniform self-stabilizing algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of an arbitrary positively real-weighted graph. Our algorithm consists in two stages of stabilizing…
Recently introduced and studied in arXiv:2407.07888, a self-similar Markov tree (ssMt) is a random decorated tree that vastly generalises the fragmentation tree. We study here the critical case that was left aside in arXiv:2407.07888.…
A simple Rouse-type model, generalised to incorporate the effects of chemical crosslinks, is used to obtain a theoretical prediction for the critical behaviour of the normal-stress coefficients $\Psi_{1}$ and $\Psi_{2}$ at the gelation…
Motivated by the problem of routing reliably and scalably in a graph, we introduce the notion of a splicer, the union of spanning trees of a graph. We prove that for any bounded-degree n-vertex graph, the union of two random spanning trees…
Considered are the large $N$, or large intensity, forms of the distribution of the length of the longest increasing subsequences for various models. Earlier work has established that after centring and scaling, the limit laws for these…
The goal of these lectures is to survey some of the recent progress on the description of large-scale structure of random trees. We use the framework of Markov-Branching sequences of trees and discuss several applications.
For some discretely observed path of oscillating Brownian motion with level of self-organized criticality $\rho_0$, we prove in the infill asymptotics that the MLE is $n$-consistent, where $n$ denotes the sample size, and derive its limit…
The first part of this paper ( arXiv:1607.02114 ) introduced splitting trees, those chronological trees admitting the self-similarity property where individuals give birth, at constant rate, to iid copies of themselves. It also established…
Can we obtain a Brownian CRT of mass $1/2$ from a CRT of mass $1$ by cutting certain branches? In this paper, we will answer that question in the much more general setting of self-similar Markov trees. Self-similar Markov trees (ssMt) are…
The paper deals with non-linear Poisson neuron network models with bounded memory dynamics, that can include both Hebbian learning mechanisms and refractory periods. The state of a network is described by the times elapsed since its neurons…
Consider the edge-deletion process in which the edges of some finite tree T are removed one after the other in the uniform random order. Roughly speaking, the cut-tree then describes the genealogy of connected components appearing in this…
Stochastic networks based on random point sets as nodes have attracted considerable interest in many applications, particularly in communication networks, including wireless sensor networks, peer-to-peer networks and so on. The study of…
The Feller diffusion is studied as the limit of a coalescent point process in which the density of the node height distribution is skewed towards zero. Using a unified approach, a number of recent results pertaining to scaling limits of…
We consider two classes of natural stochastic processes on finite unlabeled graphs. These are Euclidean stochastic optimization algorithms on the adjacency matrix of weighted graphs and a modified version of the Metropolis MCMC algorithm on…
The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…
Steady statistics of a passive scalar advected by a random two-dimensional flow of an incompressible fluid is described in the range of scales between the correlation length of the flow and the diffusion scale. That corresponds to the…
Consider a Markov chain $(\xi_v)_{v \in V} \in [k]^V$ on the infinite $b$-ary tree $T = (V,E)$ with irreducible edge transition matrix $M$, where $b \geq 2$, $k \geq 2$ and $[k] = \{1,...,k\}$. We denote by $L_n$ the level-$n$ vertices of…