Related papers: The initial set in the frog model is irrelevant
A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…
In this paper we review a series of results obtained for 1D and 2D simple N-body dynamical models with infinite-range attractive interactions and without short distance singularities. The free energy of both models can be exactly obtained…
We identify general conditions under which regenerative processes with dependent cycles and cycle lengths are asymptotically independent. The result is applied to various models. In particular, independent L\'evy processes with dependent…
Place an active particle at the root of the infinite $d$-ary tree and dormant particles at each non-root site. Active particles move towards the root with probability $p$ and otherwise move to a uniformly sampled child vertex. When an…
At the limit of an infinite confinement strength $\omega$, the ground state of a system that comprises two fermions or bosons in a harmonic confinement interacting through the Fermi--Huang pseudopotential remains strongly correlated. A…
Pair interactions between active particles need not follow Newton's third law. In this work we propose a continuum model of pattern formation due to non-reciprocal interaction between multiple species of scalar active matter. The classical…
A protein model with the pairwise interaction energies varying as local environment changes, i.e., including some kinds of collective effect between the contacts, is proposed. Lattice Monte Carlo simulations on the thermodynamical…
We study a continuous time Mutually Catalytic Branching model on the $\mathbb{Z}^{d}$. The model describes the behavior of two different populations of particles, performing random walk on the lattice in the presence of branching, that is,…
Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…
We study the fluctuations of a random surface in a stochastic growth model on a system of interlacing particles placed on a two dimensional lattice. There are two different types of particles, one with a low jump rate and the other with a…
Assuming the obvious definitions (see paper) we show the a decidable model that is effectively prime is also effectively atomic. This implies that two effectively prime (decidable) models are computably isomorphic. This is in contrast to…
We extract the long-distance asymptotic behaviour of two-point correlation functions in massless quantum integrable models containing multi-species excitations. For such a purpose, we extend to these models the method of a large-distance…
We report on a study of a classical, finite system of confined particles in two dimensions with a two-body repulsive interaction. We first develop a simple analytical method to obtain equilibrium configurations and energies for few…
In this paper we consider the conformal dynamics for a system of $N$ interacting relativistic massless particles. A detailed study is done for the case of two-particles, with a particular attention to the symmetries of the problem. In fact,…
Consider the ideal I corresponding to r points in P^2. We study the symbolic generic initial system of I, formed by taking the generic initial ideals of the symbolic powers of I, and its asymptotic behaviour. In particular, we describe the…
We study the collective behavior of nonequilibrium systems subject to an external field with a dynamics characterized by the existence of non-interacting states. Aiming at exploring the generality of the results, we consider two types of…
The entanglement of two dipole-coupled atoms with nondegenerate two-photon transitions interacting with two-mode field in lossless cavity has been investigated. It shows that the entanglement is dependent on the initial atomic states. The…
We study the frog model on $\mathbb{Z}$ with particle-wise random geometric lifetimes: each particle has a survival parameter $\pi\in(0,1)$ sampled i.i.d., whose density near $1$ satisfies $f_\pi(u)\sim (1-u)^{\beta-1}L\big((1-u)^{-1}\big)$…
The paired state of composite fermions is expected to support two kinds of excitations: vortices and unpaired composite fermions. We construct an explicit microscopic description of the unpaired composite fermions, which we demonstrate to…
We consider a model of fermions interacting via point interactions, defined via a certain weighted Dirichlet form. While for two particles the interaction corresponds to infinite scattering length, the presence of further particles…