Related papers: Concentration results for directed polymer with un…
We study a model of directed polymers with an exponentially recurrent Markov chain and an indefinitely divisible random environment. We prove that the normalized partition function converges exponentially fast towards zero at all…
Temporal correlation for randomly growing interfaces in the KPZ universality class is a topic of recent interest. Most of the works so far have been concentrated on the zero temperature model of exponential last passage percolation, and…
We consider the escape of a flexible, self-avoiding polymer chain out of a confined geometry. By means of simulations, we demonstrate that the translocation time can be described by a simple scaling law that exhibits a nonlinear dependence…
Consider directed polymers in a random environment on the complete graph of size $N$. This model can be formulated as a product of i.i.d. $N\times N$ random matrices and its large time asymptotics is captured by Lyapunov exponents and the…
We consider a directed random walk model of a random heterogeneous polymer in the proximity of an interface separating two selective solvents. This model exhibits a localization/delocalization transition. A positive value of the free energy…
For directed polymers, the shape function computes the limiting average energy accrued by paths with a given average slope. We prove that, for a large family of directed polymer models in discrete time and continuous space in dimension…
Probabilistic models of directed polymers in random environment have received considerable attention in recent years. Much of this attention has focused on integrable models. In this paper, we introduce some new computational tools that do…
The joint statistical properties of two free energies computed at two different temperatures in {\it the same sample} of $(1+1)$ directed polymers is studied in terms of the replica technique. The scaling dependence of the reduced free…
During fast diffusion-influenced polymerization, nonequilibrium behavior of the polymer chains and the surrounding reactive monomers has been reported recently. Based on the laws of thermodynamics, the emerging nonequilibrium structures…
Understanding and computing the entropic forces exerted by polymer chains under confinement is important for many reasons, from research to applications. However, extracting properties related to the free energy, such as the force (or…
We study the scaling exponents of a 1+1-dimensional directed polymer in a Brownian random environment introduced by O'Connell and Yor. For a version of the model with boundary conditions that are stationary in a space-time sense we identify…
We study the partition function of two versions of the continuum directed polymer in 1+1 dimension. In the full-space version, the polymer starts at the origin and is free to move transversally in the reals, and in the half-space version,…
We study the directed polymer model in a bounded environment in weak disorder but without $L^2$-boundedness, specifically the speed of homogenization for the field $(W_n^{0,x})_{x\in\mathbb Z^d}$, where $W_n^{0,x}$ denotes the associated…
We investigate the high-temperature behavior of the directed polymer model in dimension $1+2$. More precisely we study the difference $\Delta \mathtt{F}(\beta)$ between the quenched and annealed free energies for small values of the inverse…
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…
In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy \[H_n=\sum_{1\le j<k\le n}\omega_j\omega_k1_{\{S_j=S_k\}}\] of the polymer $\{S_1,...,S_n\}$ equipped with random…
A directed polymer is allowed to branch, with configurations determined by global energy optimization and disorder. A finite size scaling analysis in 2D shows that, if disorder makes branching more and more favorable, a critical transition…
In this paper we consider a two-dimensional model of a copolymer consisting of a random concatenation of hydrophilic and hydrophobic monomers, immersed in a micro-emulsion of random droplets of oil and water. The copolymer interacts with…
The aim of this paper is to investigate the distribution of a continuous polymer in the presence of an attractive finitely supported potential. The most intricate behavior can be observed if we simultaneously and independently vary two…
We study the semi-discrete directed polymer model introduced by O'Connell-Yor in its stationary regime, based on our previous work on the stationary $q$-totally asymmetric simple exclusion process ($q$-TASEP) using a two-sided $q$-Whittaker…