Related papers: Periodic KPZ fixed point with general initial cond…
Height fluctuations are studied in the one-dimensional totally asymmetric simple exclusion process with periodic boundaries, with a focus on how late time relaxation towards the non-equilibrium steady state depends on the initial condition.…
In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…
We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…
This paper investigates a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of the admissible statistical averages of probability…
We discuss the non-self-averaging phenomena in the critical point of weakly disordered Ising ferromagnet. In terms of the renormalized replica Ginzburg-Landau Hamiltonian in dimensions D <4, we derive an explicit expression for the…
We consider the KPZ equation in one space dimension driven by a stationary centred space-time random field, which is sufficiently integrable and mixing, but not necessarily Gaussian. We show that, in the weakly asymmetric regime, the…
We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the…
The Kardar-Parisi-Zhang (KPZ) class is a paradigmatic example of universality in nonequilibrium phenomena, but clear experimental evidences of asymptotic 2D-KPZ statistics are still very rare, and far less understanding stems from its…
This paper deals with a one--dimensional model for granular materials, which boils down to an inelastic version of the Kac kinetic equation, with inelasticity parameter $p>0$. In particular, the paper provides bounds for certain distances…
The one-dimensional totally asymmetric simple exclusion process (TASEP) with $N$ particles on a periodic lattice of $L$ sites is an interacting particle system with hopping rates breaking detailed balance. The total time-integrated current…
We consider the totally asymmetric simple exclusion process, a model in the KPZ universality class. We focus on the fluctuations of particle positions starting with certain deterministic initial conditions. For large time t, one has regions…
We study a stochastic PDE model for an evolving set $\mathbb{M}(t)\subseteq\mathbb{R}^{\mathrm{d}+1}$ that resembles a continuum version of origin-excited or reinforced random walk. We show that long-time fluctuations of an associated…
The phase diagram of a dissipative particle in a periodic potential and a magnetic field is studied in the weak barrier limit and in the tight-biding regime. For the case of half flux per plaquette, and for a wide range of values of the…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
We study the asymmetric simple exclusion process (ASEP) on a segment $\{1,\ldots,b_N\}$ and are interested in its total variation distance to equilibrium when started from an initial configuration $\xi^{N}$. We provide a general result…
We consider the half-space geometric Last Passage Percolation model starting with stationary measures. We obtain exact formulas for LPP value along the diagonal $(N,N)$ across the entire phase diagram. We also obtain the limits of these…
We consider interacting many particle systems with quenched disorder having strong Griffiths singularities, which are characterized by the dynamical exponent, z, such as random quantum systems and exclusion processes. In several d=1 and d=2…
The existence of nonzero localised periodic solutions for general one-dimensional discrete nonlinear Klein-Gordon systems with convex on-site potentials is proved. The existence problem of localised solutions is expressed in terms of a…
We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…
We provide an introduction of some basic facts of uniformly almost periodic functions, such as Fourier series representations. A result is then proved about Fourier coefficients which is a generalization of the purely periodic case. We then…