相关论文: A short proof of diffusivity for the directed poly…
Talk presented at the International Conference on Mathematical Physics (Brisbane 1997). This is an introduction to recent work on the scaling and intermittency in forced Burgers turbulence. The mapping between Burgers' equation and the…
We present some recent results concerning the persistence of dynamical localization for disordered systems of n particles under weak interactions.
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
In this letter, we study the effects of weak off-diagonal disorder on conjugated polymers with a doubly degenerate ground-state. We find that disorder induces a finite density of neutral solitons in the lattice dimerization of a polymer…
We investigate the dynamics of a particle moving randomly along a disordered hetero-polymer subjected to rapid conformational changes which induce superdiffusive motion in chemical coordinates. We study the antagonistic interplay between…
The nature of glass phases of liquid crystals in random porous media depends on the effective disorder strength. We study how the disorder strength depends on the density of the porous media and demonstrate that it can increase as the…
In this paper we prove a scaling limit phase transition for a class of two-dimensional random polymers.
We study discrete linear divergence-form operators with random coefficients, also known as the random conductance model. We assume that the conductances are bounded, independent and stationary; the law of a conductance may depend on the…
We describe some recent results concerning the statistical properties of a self-interacting polymer stretched by an external force. We concentrate mainly on the cases of purely attractive or purely repulsive self-interactions, but our…
A copolymer is a chain of repetitive units (monomers) that are almost identical, but they differ in their degree of affinity for certain solvents. This difference leads to striking phenomena when the polymer fluctuates in a nonhomogeneous…
We calculate exactly the velocity and diffusion constant of a microscopic stochastic model of $N$ evolving particles which can be described by a noisy traveling wave equation with a noise of order $N^{-1/2}$. Our model can be viewed as the…
We examine the applicability of the weak wave turbulence theory in explaining experimental scaling results obtained for the diffusion and relative diffusion of particles moving on turbulent surface waves. For capillary waves our theoretical…
In this paper, we prove convergence in distribution of Langevin processes in the overdamped asymptotics. The proof relies on the classical perturbed test function (or corrector) method, which is used both to show tightness in path space,…
We review recent experiments that provide evidence for a transition to a conducting phase in two dimensions at very low electron densities. The nature of this phase is not understood, and is currently the focus of intense theoretical and…
A systematic analysis of large scale fluctuations in the low temperature pinned phase of a directed polymer in a random potential is described. These fluctuations come from rare regions with nearly degenerate ``ground states''. The…
We study the fluctuations of the directed polymer in 1+1 dimensions in a Gaussian random environment with a finite correlation length {\xi} and at finite temperature. We address the correspondence between the geometrical transverse…
We introduce a new disorder regime for directed polymers with one space and one time dimension that is accessed by scaling the inverse temperature parameter \beta with the length of the polymer n. We scale \beta_n := \beta n^{-\alpha} for…
We state and prove a version of Dyson's Lemma for a product of smooth projective varieties of arbitrary dimension using positivity methods.
We present mathematical proofs on the existence and uniqueness of weak solutions for a special class of non linear parabolic and hyperbolic equations of mathematical physics subject to colored noise (structured turbulence) as random-…
The recently proposed universal relations between the moments of the polydispersity distributions of a phase-separated weakly polydisperse system are analyzed in detail using the numerical results obtained by solving a simple density…