Related papers: Lower large deviations for the maximal flow throug…
We consider simple exclusion processes on Z for which the underlying random walk has a finite first moment and a non-zero mean and whose initial distributions are product measures with different densities to the left and to the right of the…
We study low-Reynolds-number fluid flow through a two-dimensional porous medium modeled as a Lorentz gas. Using extensive finite element simulations we fully resolve the flow fields for packing fractions approaching the percolation…
We prove that multidimensional diffusions in random environment have a limiting velocity which takes at most two different values. Further, in the two-dimensional case we show that for any direction, the probability to escape to infinity in…
Using martingale methods, we obtain some upper bounds for large and moderate deviations of products of independent and identically distributed elements of GL d (R). We investigate all the possible moment conditions, from super-exponential…
An inverse cascade - energy transfer to progressively larger scales - is a salient feature of two-dimensional turbulence. If the cascade reaches the system scale, it creates a coherent flow expected to have the largest available scale and…
The non-random fluctuation is one of the central objects in first passage percolation. It was proved in [Shuta Nakajima. Divergence of non-random fluctuation in First Passage Percolation. {\em Electron. Commun. Probab.} 24 (65), 1-13.…
Using a weak convergence approach, we establish a Large Deviation Principle (LDP) for the solutions of fluid dynamic systems in two-dimensional bounded domains subjected to no-slip boundary conditions and perturbed by additive noise. Our…
We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law conservation law. When the…
Directed last passage percolation models on the plane, where one studies the weight as well as the geometry of optimizing paths (called polymers) in a field of i.i.d. weights, are paradigm examples of models in the KPZ universality class.…
We study the site version of (independent) first-passage percolation on the triangular lattice $\mathbb{T}$. Denote the passage time of the site $v$ in $\mathbb{T}$ by $t(v)$, and assume that $P(t(v)=0)=P(t(v)=1)=1/2$. Denote by $a_{0,n}$…
Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large…
Enumeration of various types of lattice polygons and in particular polyominoes is of primary importance in many machine learning, pattern recognition, and geometric analysis problems. In this work, we develop a large deviation principle for…
In this paper we consider a smooth flow $(\Lambda,\Phi^t)$ builded from suspending over a (non-invertible topologically mixing) subshift of finite type, and we equip it with an equilibrium measure $\nu$ on $\Lambda.$ The two main theorems…
We study the large deviation rate functional for the empirical distribution of independent Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier and Zimmer that this functional is asymptotically…
We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…
We derive some large deviation bounds for events related to the "true self-repelling motion", a one-dimensional self-interacting process introduced by Toth and Werner, that has very different path properties than usual diffusion processes.…
Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter $\theta$ approaches infinity. The motivation for these results is to understand the…
The transition of the flow in a duct of square cross-section is studied. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers; this flow is thus a good candidate to investigate the 'bypass' path…
We study the error of the number of points of a lattice $L$ that belong to a rectangle, centred at $0$, whose axes are parallel to the coordinate axes, dilated by a factor $t$ and then translated by a vector $X \in \mathbb{R}^{2}$. When we…
We study a system of hard rods of finite size in one space dimension, which move by Brownian noise while avoiding overlap. We consider a scaling in which the number of particles tends to infinity while the volume fraction of the rods…