Related papers: A short proof of diffusivity for the directed poly…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
We consider the statistical mechanics of a random polymer with random walks and disorders in $\mathbb{Z}^d$. The walk collects random disorders along the way and gets nothing if it visits the same site twice. In the continuum and weak…
We consider directed polymer models involving multiple non-intersecting random walks moving through a space-time disordered environment in one spatial dimension. For a single random walk, Alberts, Khanin and Quastel proved that under…
We expose here a short proof of Cramer's theorem in R based on convex duality.
In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques, we transform the problem to a particular…
Particles driven through a periodic potential by an external constant force are known to exhibit a pronounced peak of the diffusion around a critical force that defines the transition between locked and running states. It has recently been…
We consider a linear polymer chain in a disordered environment modeled by percolation clusters on a square lattice. The disordered environment is meant to roughly represent molecular crowding as seen in cells. The model may be viewed as the…
We consider the empirical process G_t of a one-dimensional diffusion with finite speed measure, indexed by a collection of functions F. By the central limit theorem for diffusions, the finite-dimensional distributions of G_t converge weakly…
In this paper we establish in the fast diffusion range the higher integrability of the spatial gradient of weak solutions to porous medium systems. The result comes along with an explicit reverse H\"older inequality for the gradient. The…
We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The…
We consider field theory formulation for directed polymers and interfaces in the presence of quenched disorder. We write a series representation for the averaged free energy, where all the integer moments of the partition function of the…
We study the effects of disorder on strongly coupled compressible matter in 2+1 dimensions. Our system consists of a D3/D5 intersection at finite temperature and in the presence of a disordered chemical potential. We first study the impact…
The statistical mechanics of directed line-like objects, such as directed polymers in an external field, strands of dipoles in both ferro- and electrorheological fluids, and flux lines in high-$T_{\tiny C}$ superconductors bears a close…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.
In three-dimensional materials with a Dirac spectrum, weak short-ranged disorder is essentially irrelevant near the Dirac point. This is manifestly not the case for Coulomb disorder, where the long-ranged nature of the potential produced by…
Disorder is more the rule than the exception in natural and synthetic materials. Nonetheless, wave propagation within inhomogeneously disordered materials has received scant attention. We combine microwave experiments and theory to find the…
We give a new proof of the existence of designs, which is much shorter and gives better bounds.
Predicting and controlling the transport of colloids in porous media is essential for applications ranging from contaminant remediation to drug delivery. In these complex environments, solute gradients are ubiquitous and could drive…
Doped organic semiconductors are critical to emerging device applications, including thermoelectrics, bioelectronics, and neuromorphic computing devices. It is commonly assumed that low conductivities in these materials result primarily…