Related papers: Effective diffusivities in periodic KPZ
In this paper we discuss the notion of the diffusive capacity for the generalized Forchheimer flow of fluid through porous media. The diffusive capacity is an integral characteristic of the flow motivated by the engineering notion of 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 study the directed polymer of length $t$ in a random potential with fixed endpoints in dimension 1+1 in the continuum and on the square lattice, by analytical and numerical methods. The universal regime of high temperature $T$ is…
We consider two models of random diffusion in random environment in two dimensions. The first example is the self-repelling Brownian polymer, this describes a diffusion pushed by the negative gradient of its own occupation time measure…
We prove a polynomial upper bound for the localization length of the Lorentz mirror model and the Manhattan model on the even cylinder. The main input is a conditional cylinder-localization theorem in the winding regime: if short-direction…
We provide a new construction of Brownian disks in terms of forests of continuous random trees equipped with nonnegative labels corresponding to distances from a distinguished point uniformly distributed on the boundary of the disk. This…
The first goal of this paper is to prove multiple asymptotic results for a time-discrete and space-continuous polymer model of a random walk in a random potential. These results include: existence of deterministic free energy density in the…
In last passage percolation models lying in the KPZ universality class, the energy of long energy-maximizing paths may be studied as a function of the paths' pair of endpoint locations. Scaled coordinates may be introduced, so that these…
We study the joint probability distribution function (pdf) of the maximum M of the height and its position X_M of a curved growing interface belonging to the universality class described by the Kardar-Parisi-Zhang equation in 1+1…
Fick's law for coordinate dependent diffusivity is derived. Corresponding diffusion current in the presence of coordinate dependent diffusivity is consistent with the form as given by Kramers-Moyal expansion. We have obtained the…
We prove existence and uniqueness of distributional solutions to the KPZ equation globally in space and time, with techniques from paracontrolled analysis. Our main tool for extending the analysis on the torus to the full space is a…
On the 1+2 dimensional lattice, we consider a directed polymer in a random Gaussian environment that is independent in time and correlated in space. The spatial correlation is supposed to decay as $(\log |x|)^a /|x|^{2}$, $a>-1$, where the…
We establish finite-dimensional central limit theorems for local, additive, interaction functions of temporally evolving point processes. The dynamics are those of a spatial Poisson process on the flat torus with points subject to a…
Brownian yet non-Gaussian processes have recently been observed in numerous biological systems and the corresponding theories have been built based on random diffusivity models. Considering the particularity of random diffusivity, this…
We consider the long-time behavior of a diffusion process on $\mathbb{R}^d$ advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetric in law and have a log-correlated potential. A special case…
We study the limiting probability distribution of the homogenization error for second order elliptic equations in divergence form with highly oscillatory periodic conductivity coefficients and highly oscillatory stochastic potential. The…
We compute the one-point probability distribution for the stationary KPZ equation (i.e. initial data H(0,X)=B(X), for B(X) a two-sided standard Brownian motion) and show that as time T goes to infinity, the fluctuations of the height…
We characterize the law of the partition function of a Brownian directed polymer model in terms of a diffusion process associated with the quantum Toda lattice. The proof is via a multidimensional generalization of a theorem of Matsumoto…
In this work we study the transition from normal to anomalous diffusion of Brownian particles on disordered potentials. The potential model consists of a series of "potential hills" (defined on unit cell of constant length) whose heights…
Time evolution of the position-velocity correlation functions (PVCF) plays a key role in a new formalism of Brownian motion. A system of differential equations, which governs PVCF, is derived for magnetic Skyrmions on a 2-dimensional…