A new disorder regime for directed polymers in dimension 1+1 is introduced by scaling the inverse temperature β with the length of the polymer n and interpolating between the weak disorder (β=0) and strong disorder regimes (β>0).Expand

In this paper we study the following Burgers equation
du/dt + d/dx (u^2/2) = epsilon d^2u/dx^2 + f(x,t)
where f(x,t)=dF/dx(x,t) is a random forcing function, which is periodic in x and white noise… Expand

Motivated by discrete directed polymers in one space and one time dimension, we construct a continuum directed random polymer that is modeled by a continuous path interacting with a space-time white… Expand

Abstract: We consider a spatially periodic inviscid random forced Burgers equation in arbitrary dimension and the random time-dependent Lagrangian system related to it. We construct a unique… Expand

CONTENTS § 1. Introduction § 2. Decompositions of the circle and Denjoy's theorem § 3. Density of an absolutely continuous invariant measure § 4. Proof of the main theorem § 5. Discussion of the… Expand

A simple probabilistic model for the early stage of neuron growth: the specification on an axon out of several initially similar neurites is presented, wherein longer objects have more chances to grow, and parameter α determines the intensity of the competition.Expand

CONTENTS § 1. Sequences of period-doubling bifurcations § 2. Facts from the general theory of continuous one-dimensional maps § 3. The doubling transformation § 4. Properties of the Feigenbaum… Expand

Philosophical Transactions of the Royal Society A…

4 January 2010

TLDR

It is shown that, for any convex Hamiltonian, there exists a uniquely defined canonical global non-smooth coalescing flow that extends particle trajectories and determines the dynamics inside shocks.Expand