相关论文: Geography of local configurations

We compare the behaviour of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability…

We study a new class of matrix models, formulated on a lattice. On each site are $N$ states with random energies governed by a Gaussian random matrix Hamiltonian. The states on different sites are coupled randomly. We calculate the density…

Markov chains arising from random iteration of functions $S_{\theta}:X\to X$, $\theta \in \Theta$, where $X$ is a Polish space and $\Theta$ is arbitrary set of indices are considerd. At $x\in X$, $\theta$ is sampled from distribution…

We consider a discrete random walk on a diagonal lattice in two and three dimensions and obtain explicit solutions of absorption probabilities and probabilities of return in several domains. In three dimensions we consider both the cube and…

Electromagnetic fields with complex spatial variation routinely arise in Nature. We study the response of a small molecule to monochromatic fields of arbitrary three-dimensional geometry. First, we consider the allowed configurations of the…

The problem of determining the volume of a tubular neighbourhood has a long and rich history. Bounds on the volume of neighbourhoods of algebraic sets have turned out to play an important role in the probabilistic analysis of condition…

Sites in an infinite d-dimensional lattice, open with probability greater or equal to 1/d, form an infinite open path.

We establish long-range order for discrete nearest-neighbor spin systems on $\mathbb{Z}^d$ satisfying a certain symmetry assumption, when the dimension $d$ is higher than an explicitly described threshold. The results characterize all…

We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total…

In a generalized framework, where multi-state and inter-state linkages are allowed, we derive a sufficient condition for the stability of synchronization in a network of chaotic attractors. This condition explicitly relates the network…

We use recent results that localized excitations in nonlinear Hamiltonian lattices can be viewed and described as multiple-frequency excitations. Their dynamics in phase space takes place on tori of corresponding dimension. For a…

We use recent results that localized excitations in nonlinear Hamiltonian lattices can be viewed and described as multiple-frequency excitations. Their dynamics in phase space takes place on tori of corresponding dimension. For a…

We define a general class of models representing natural selection between two alleles. The population size and spatial structure are arbitrary, but fixed. Genetics can be haploid, diploid, or otherwise; reproduction can be asexual or…

We obtain the leading orders of the maximum and the minimum of local times for the simple random walk on the two-dimensional torus at time proportional to the cover time. We also estimate the number of points with large (or small) values of…

Topology in photonics comes in two distinct flavors: global and local. Global topology considers invariants that are obtained by integrating over the energy band, whereas local topology considers defects, typically vortices, in the…

In this paper, we present a general framework for constructively proving the existence and of stationary localized solutions, spatially periodic solutions, and branches of spatially periodic solutions in the 1D Thomas model. Specifically,…

We consider two varieties of labeled rooted trees, and the probability that a vertex chosen from all vertices of all trees of a given size uniformly at random has a given rank. We prove that this probability converges to a limit as the tree…

Tight-binding 1D random system with long-range correlations is studied numerically using the localisation criterium, which represents the number of sites, covered by the wave function. At low degrees of disorder the signs of a mobility…

We show that large critical multi-type Galton-Watson trees, when conditioned to be large, converge locally in distribution to an infinite tree which is analoguous to Kesten's infinite monotype Galton-Watson tree. This is proven when we…

We study the probabilistic existence of point configurations satisfying the $(0, m, d)$-net property in base $b$ within a randomly generated point set of size $N$ in the $d$-dimensional unit cube. We first derive an upper bound on the…