Related papers: The vacant set of two-dimensional critical random …
While there exists a well-developed asymptotic theory of Fr\'echet means of random variables taking values in a general "finite-dimensional" metric space, there are only a few known results in which the random variables can take values in…
We consider independent and $m$-dependent two-dimensional oriented site percolation with open-site density close to one started from Bernoulli product measures. We show that the probability of an occupied interval in the former process…
What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems which can be solved. An example of such a system is the…
An anomalous mean-field solution is known to capture the non trivial phase diagram of the Ising model in annealed complex networks. Nevertheless the critical fluctuations in random complex networks remain mean-field. Here we show that a…
A random neighbor extremal stick-slip model is introduced. In the thermodynamic limit, the distribution of states has a simple analytical form and the mean avalanche size, as a function of the coupling parameter, is exactly calculable. The…
We consider random interlacements on Z^d, with d bigger or equal to 3, when their vacant set is in a strongly percolative regime. We derive an asymptotic upper bound on the probability that the random interlacements disconnect a box of…
We introduce the model of two-dimensional continuous random interlacements, which is constructed using the Brownian trajectories conditioned on not hitting a fixed set (usually, a disk). This model yields the local picture of Wiener sausage…
In [Kozma-Toth, Ann. Probab. v 45, pp 4307-4347 (2017)] the weak CLT was established for random walks in doubly stochastic (or, divergence-free) random environments, under the following conditions: 1. Strict ellipticity assumed for the…
We introduce the notion of a "random basic walk" on an infinite graph, give numerous examples, list potential applications, and provide detailed comparisons between the random basic walk and existing generalizations of simple random walks.…
Given a discrete random walk on a finite graph $G$, the vacant set and vacant net are, respectively, the sets of vertices and edges which remain unvisited by the walk at a given step $t$.%These sets induce subgraphs of the underlying graph.…
We study the critical breakdown of two-dimensional quantum magnets in the presence of algebraically decaying long-range interactions by investigating the transverse-field Ising model on the square and triangular lattice. This is achieved…
We study the two-dimensional Ising model on a network with a novel type of quenched topological (connectivity) disorder. We construct random lattices of constant coordination number and perform large scale Monte Carlo simulations in order…
The model considered is a d=2 layered random Ising system on a square lattice with nearest neighbours interaction. It is assumed that all the vertical couplings are equal and take the positive value J while the horizontal couplings are…
The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters…
Using inverse Ising inference we show that the absorbing states of the one-dimensional Manna model can be described by an equilibrium model with an emergent interaction displaying short-ranged repulsion and long-ranged attraction. As the…
In random sequential adsorption (RSA), objects are deposited randomly, irreversibly, and sequentially; attempts leading to an overlap with previously deposited objects are discarded. The process continues until the system reaches a jammed…
We study the critical properties of finite-dimensional dissipative quantum spin systems with uniform ferromagnetic interactions. Starting from the transverse-field Ising model coupled to a bath of harmonic oscillators with Ohmic spectral…
In this article, we study several aspects of the intersections of algorithmically random closed sets. First, we answer a question of Cenzer and Weber, showing that the operation of intersecting relatively random closed sets (with respect to…
In long-range percolation on $\mathbb{Z}^d$, points $x$ and $y$ are connected by an edge with probability $1-\exp(-\beta\|x-y\|^{-d-\alpha})$, where $\alpha>0$ is fixed and $\beta \geq 0$ is a parameter. As $d$ and $\alpha$ vary, the model…
In this paper, we show several rigorous results on the phase transition of Finitary Random Interlacement (FRI). For the high intensity regime, we show the existence of a critical fiber length, and give the exact asymptotic of it as…