Related papers: Finite range interlacements and couplings

We study the energy landscapes of particles with short-range attractive interactions as the range of the interactions increases. Starting with the set of local minima for $6\leq N\leq12$ hard spheres that are "sticky", i.e. they interact…

This paper considers an infinite system of instantaneously coalescing rate one simple random walks on $\mathbb{Z}^2$, started from the initial condition with all sites in $\mathbb{Z}^2$ occupied. We show that the correlation functions of…

We consider energies on a periodic set ${\mathcal L}$ of ${\mathbb R}^d$ of the form $\sum_{i,j\in{\mathcal L}} a^\varepsilon_{ij}|u_i-u_j|$, defined on spin functions $u_i\in\{0,1\}$, and we suppose that the typical range of the…

In \cite{SzT}, D. Sz\'asz and A. Telcs have shown that for the diffusively scaled, simple symmetric random walk, weak convergence to the Brownian motion holds even in the case of local impurities if $d \ge 2$. The extension of their result…

Let $\tau = (\tau_i : i \in {\Bbb Z})$ denote i.i.d.~positive random variables with common distribution $F$ and (conditional on $\tau$) let $X = (X_t : t\geq0, X_0=0)$, be a continuous-time simple symmetric random walk on ${\Bbb Z}$ with…

The potential of the process $\gamma \gamma \rightarrow \tau \bar{\tau}\gamma$ is examined in a model-independent way using the effective Lagrangian approach for the ILC which is designed with standard configurations of 0.25 TeV/2000…

Motivated by its relevance for the study of perturbations of one-dimensional voter models, including stochastic Potts models at low temperature, we consider diffusively rescaled coalescing random walks with branching and killing. Our main…

This article investigates the effect for random pinning models of long range power-law decaying correlations in the environment. For a particular type of environment based on a renewal construction, we are able to sharply describe the phase…

The conventional parametrizations of lattice static interquark force are shown to produce a mismatch of coupling constant near the matching point R_m \approx 0.2 fm. The running coupling constant of the background perturbation theory yields…

We consider branching random walks on the Euclidean lattice in dimensions five and higher. In this non-Markovian setting, we first obtain a relationship between the equilibrium measure and Green's function, in the form of an approximate…

To allow for a comparison of theoretical predictions for spin chains with experimental data, it is often important to take impurity effects as well as interchain couplings into account. Here we present the field theory for finite spin…

The recent LEP data for gauge coupling constants constrain many grand unified models. In this paper, we study several possibilities for unification of gauge coupling constants. Without an intermediate mass scale, the minimal supersymmetric…

We study simple nonequilibrium distributions describing a classical gas of particles interacting via a pair potential ${\phi}(x/{\epsilon})$, in the Boltzmann-Grad scaling ${\epsilon} \rightarrow 0$. We establish bounds for truncated…

We consider the percolation problem of sites on an $L\times L$ square lattice with periodic boundary conditions which were unvisited by a random walk of $N=uL^2$ steps, i.e. are vacant. Most of the results are obtained from numerical…

Given two independent Poisson point processes $\Phi^{(1)},\Phi^{(2)}$ in $R^d$, the continuum AB percolation model is the graph with points of $\Phi^{(1)}$ as vertices and with edges between any pair of points for which the intersection of…

We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise, in the limit of large N. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest…

We consider a system of asymmetric independent random walks on $\mathbb{Z}^d$, denoted by $\{\eta_t,t\in{\mathbb{R}}\}$, stationary under the product Poisson measure $\nu_{\rho}$ of marginal density $\rho>0$. We fix a pattern $\mathcal{A}$,…

Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…

We correct and streamline the proof of the fact that, at the critical point $\alpha=1$, the vacant set of the two-dimensional random interlacements is infinite (Comets, Popov, 2017). Also, we prove a zero-one law for a natural class of tail…

In this paper, we prove the exact orders of critical intensity $u_*(T)$ in Finitary Random Interlacements (FRI) in $\mathbb{Z}^d, \ d\ge 3$ with respect to the expected fiber length $T$. We show that as $T\to\infty$, $u_*(T)\sim T^{-1}, \…