Related papers: Maximal spanning time for neighborhood growth on t…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
A lattice model of critical spanning webs is considered for the finite cylinder geometry. Due to the presence of cycles, the model is a generalization of the known spanning tree model which belongs to the class of logarithmic theories with…
Let $M = \mathbb{B}^2 / \Gamma$ be a smooth ball quotient of finite volume with first betti number $b_1(M)$ and let $\mathcal{E}(M) \ge 0$ be the number of cusps (i.e., topological ends) of $M$. We study the growth rates that are possible…
We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (U) and nearest-neighbor (V) interactions, at weak couplings. We show that the charge-density-wave phase that is known to occur…
We consider the hard-core model on finite triangular lattices with Metropolis dynamics. Under suitable conditions on the triangular lattice dimensions, this interacting particle system has three maximum-occupancy configurations and we…
Let $X^1, ..., X^k$ and $Y^1, ..., Y^m$ be jointly independent copies of random variables $X$ and $Y$, respectively. For a fixed total number $n$ of random variables, we aim at maximising $M(k,m):= E \max \{X^1, ..., X^k, Y^1, >..., Y^{m}…
We consider the lattice dynamics in the harmonic approximation for We consider the lattice dynamics in the harmonic approximation for a simple hypercubic lattice with arbitrary unit cell. The initial data are random according to a…
We study the formation of domain walls in a phase transition in which an S_5\times Z_2 symmetry is spontaneously broken to S_3\times S_2. In one compact spatial dimension we observe the formation of a stable domain wall lattice. In two…
We use numerical Monte Carlo simulation to study kinetics of deposition of oriented superdisks, bounded by the Lame curves of the form $|x|^{2p}+|y|^{2p}=1$, on regular planar substrate. It was recently shown that the maximum packing…
We consider a generic one dimensional spin system of length $ L $, arbitrarily large, with strictly local interactions, for example nearest neighbor, and prove that the dynamical $ \alpha $-R\'enyi entropies, $ 0 < \alpha \le 1 $, of an…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
We present the first example where length scale for the growth of ordered regions and the correlation length for the two point correlations of persistent sites scale differently with time. We do so by studying a global spin exchange…
Strongly long-range interacting quantum systems---those with interactions decaying as a power-law $1/r^{\alpha}$ in the distance $r$ on a $D$-dimensional lattice for $\alpha\le D$---have received significant interest in recent years. They…
We consider the Cauchy problem for two prototypes of flux-saturated diffusion equations. In arbitrary space dimension, we give an optimal condition on the growth of the initial datum which discriminates between occurrence or nonoccurrence…
We consider models of evolving networks $\{\mathcal{G}_n:n\geq 0\}$ modulated by two parameters: an attachment function $f:\mathbb{N}_0\to\mathbb{R}_+$ and a (possibly random) attachment sequence $\{m_i:i\geq 1\}$. Starting with a single…
The coupled map lattice by Olami {\it et al.} [Phys. Rev. Lett. {\bf 68}, 1244 (1992)] is ``doped'' by letting just {\it one} site have a threshold, $T^{*}_{\rm max}$, bigger than the others. On an $L \times L$ lattice with periodic…
We consider a model of long-range first-passage percolation on the $d$ dimensional square lattice $Z^d$ in which any two distinct vertices $x, y \in Z^d$ are connected by an edge having exponentially distributed passage time with mean…
We investigate a Hamiltonian lattice version of the two-dimensional Wess-Zumino model by Quantum Monte Carlo simulations. In order to study the pattern of supersymmetry breaking, we measure the ground state energy and the correlation length…
The growth of multicomponent structures in simulations and experiments often results in kinetically trapped, nonequilibrium objects. In such cases we have no general theoretical framework for predicting the outcome of the growth process.…
We revisit the classic Maximum $k$-Coverage problem: Determine the largest number $t$ of elements that can be covered by choosing $k$ sets from a given family $\mathcal{F} = \{S_1,\dots, S_n\}$ of a size-$u$ universe. A notable special case…