Related papers: Infinite Volume Continuum Random Cluster Model
The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…
A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce…
A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce…
We prove the following conjecture of Margulis. Let $G$ be a higher rank simple Lie group and let $\Lambda\le G$ be a discrete subgroup of infinite covolume. Then, the locally symmetric space $\Lambda\backslash G/K$ admits injected balls of…
I show that frequentism, as an explanation of probability in classical statistical mechanics, can be extended in a natural way to a decoherent quantum history space, the analogue of a classical phase space. The result is a form of finite…
We state the Central Limit Theorem, as the degree goes to infinity, for the normalized volume of the zero set of a rectangular Kostlan-Shub-Smale random polynomial system. This paper is a continuation of {\it Central Limit Theorem for the…
Clustering is an important phenomenon in turbulent flows laden with inertial particles. Although this process has been studied extensively, there are still open questions about both the fundamental physics and the reconciliation of…
We derive an asymptotic expansion for the critical percolation density of the random connection model as the dimension of the encapsulating space tends to infinity. We calculate rigorously the first expansion terms for the Gilbert disk…
A consistent theory, which describes the incoherent scattering of classically moving relativistic particles by the nuclei of crystal planes without any phenomenological parameter is presented. The basic notions of quantum mechanics are…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical…
We consider a one-dimensional interacting spinless fermion model, which displays the well-known Luttinger liquid (LL) to charge density wave (CDW) transition as a function of the ratio between the strength of the interaction, $U$, and the…
The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$…
The contact model for the spread of disease may be viewed as a directed percolation model on $\ZZ \times \RR$ in which the continuum axis is oriented in the direction of increasing time. Techniques from percolation have enabled a fairly…
The existence and exact form of the continuum expression of the discrete nonlogarithmic $q$-entropy is an important open problem in generalized thermostatistics, since its possible lack implies that nonlogarithmic $q$-entropy is irrelevant…
In this paper, we present a cluster algorithm for the numerical simulations of non-additive hard-core mixtures. This algorithm allows one to simulate and equilibrate systems with a number of particles two orders of magnitude larger than…
We study the long-time behavior of a particle in $\mathbb{R}^d$, $d \geq 2$, subject to molecular diffusion and advection by a random incompressible flow. The velocity field is the divergence of a stationary random stream matrix $\mathbf{k}…
Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and…
We discuss the notion of bound entanglement (BE) for continuous variables (CV). We show that the set of non--distillable states (NDS) for CV is nowhere dense in the set of all states, i.e., the states of infinite--dimensional bipartite…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…