相关论文: Diffusive limits on the Penrose tiling

I review some recent lattice results on studying chiral and deconfinement transition in QCD at finite temperature and density, as well as properties of strongly interacting matter at high temperatures. I discuss lattice results on the…

We study the phase transition phenomena for long-range oriented percolation and contact process. We studied a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution $N$. We also…

We consider random walks in dynamic random environments given by Markovian dynamics on $\mathbb{Z}^d$. We assume that the environment has a stationary distribution $\mu$ and satisfies the Poincar\'e inequality w.r.t. $\mu$. The random walk…

For a long time one has associated to the Quantum Heisenberg Ferromagnet on a lattice, a random walk on the permutation group of the lattice vertices. We here present a polymer expansion for the solution of the heat equation coupled to the…

We study a discrete random walk on a one-dimensional finite lattice, where each state has different probabilities to move one step forward, backward, staying for a moment or being absorbed. We obtain expected number of arrivals and expected…

This paper considers the problem of estimating probability density functions on the rotation group $SO(3)$. Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel.…

We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central…

The phase diagram and the thermodynamics of the random field Ising model (RFIM) defined on a family of diamond hierarchical lattices of arbitrary dimension and scaling factor $b=2$ is investigated. The phase diagram is studied considering…

We present numerical calculations of electronic structure and transport in Penrose approximants. The electronic structure of perfect approximants shows a spiky density of states and a tendency to localization that is more pronounced in the…

We study random walks on the integers driven by a sample of time-dependent nearest-neighbor conductances that are bounded but are permitted to vanish over time intervals of positive Lebesgue-length. Assuming only ergodicity of the…

We consider quantum walks with position dependent coin on 1D lattice $\mathbb{Z}$. The dispersive estimate $\|U^tP_c u_0\|_{l^\infty}\lesssim (1+|t|)^{-1/3} \|u_0\|_{l^1}$ is shown under $l^{1,1}$ perturbation for the generic case and…

We consider a model for random walks on random environments (RWRE) with random subset of Z^d as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the d coordinate directions). We…

It is well known that a positive proportion of all points in a $d$-dimensional lattice is visible from the origin, and that these visible lattice points have constant density in $\mathbb{R}^d$. In the present paper we prove an analogous…

Elements of the pomeron phenomenology within the Regge pole exchange picture are recalled. This includes discussion of the high energy behaviour of total cross-sections, the triple pomeron limit of the diffractive dissociation and the…

We investigate percolation on a randomly directed lattice, an intermediate between standard percolation and directed percolation, focusing on the isotropic case in which bonds on opposite directions occur with the same probability. We…

We consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\eta$ which breaks the…

In this paper we introduce a variant of the honeycomb lattice in which we create defects by randomly exchanging adjacent bonds, producing a random tiling with a distribution of polygon edges. We study the percolation properties on these…

We consider a Markov evolution of lozenge tilings of a quarter-plane and study its asymptotics at large times. One of the boundary rays serves as a reflecting wall. We observe frozen and liquid regions, prove convergence of the local…

Various unusual behaviors of artificial materials are governed by their topological properties, among which the edge state at the boundary of a photonic or phononic lattice has been captivated as a popular notion. However, this remarkable…

We perform numerical scattering experiments on a Lorentz array of disks centered on a triangular lattice with L columns and study its transmission and reflection properties. In the finite horizon case, the motion of the particles may be…