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In this paper, we consider directed polymers in random environment with discrete space and time. For transverse dimension at least equal to 3, we prove that diffusivity holds for the path in the full weak disorder region, i.e., where the…

Probability · Mathematics 2007-05-23 Francis Comets , Nobuo Yoshida

We consider a one-dimensional directed polymer in a random potential which is characterized by the Gaussian statistics with the finite size local correlations. It is shown that the well-known Kardar's solution obtained originally for a…

Statistical Mechanics · Physics 2009-10-30 S. E. Korshunov , Vik. S. Dotsenko

We study the directed polymer with fixed endpoints near an absorbing wall, in the continuum and in presence of disorder, equivalent to the KPZ equation on the half space with droplet initial conditions. From a Bethe Ansatz solution of the…

Disordered Systems and Neural Networks · Physics 2015-06-11 Thomas Gueudre , Pierre Le Doussal

In this paper, we study the so-called intermediate disorder regime for a directed polymer in a random environment with heavy-tail. Consider a simple symmetric random walk $(S_n)_{n\geq 0}$ on $\mathbb{Z}^d$, with $d\geq 1$, and modify its…

Probability · Mathematics 2021-04-28 Quentin Berger , Hubert Lacoin

In this paper we consider in detail the connection between the problem of a polymer in a random medium and that of a quantum particle in a random potential. We are interested in a system of finite volume where the polymer is known to be…

Disordered Systems and Neural Networks · Physics 2009-10-31 Yohannes Shiferaw , Yadin Y. Goldschmidt

This paper describes directed polymer on general time-correlated random field. Law of large numbers, existence and smoothness of limiting free energies are proved at all temperature. We also display the delocalized-localized transition, via…

Probability · Mathematics 2024-12-20 Jiaming Chen

We consider a directed polymer model in dimension $1+1$, where the disorder is given by the occupation field of a Poisson system of independent random walks on $\mathbb Z$. In a suitable continuum and weak disorder limit, we show that the…

Probability · Mathematics 2021-04-20 Hao Shen , Jian Song , Rongfeng Sun , Lihu Xu

We present using simple scaling arguments and one step replica symmetry breaking a theory for the localization of semiflexible polymers in a quenched random environment. In contrast to completely flexible polymers, localization of…

Soft Condensed Matter · Physics 2009-11-10 Arti Dua , Thomas A. Vilgis

We present results about large deviations and laws of large numbers for various polymer related quantities. In a completely general setting and strictly positive temperature, we present results about large deviations for directed polymers…

Probability · Mathematics 2012-10-03 Nicos Georgiou

We analyze the localized phase of a general model of a directed polymer in the proximity of an interface that separates two solvents. Each monomer unit carries a charge, $\omega_n$, that determines the type (attractive or repulsive) and the…

Probability · Mathematics 2007-05-23 G. Giacomin , F. L. Toninelli

We consider the directed polymer model in the weak disorder phase under the assumption that the partition function is $L^p$-bounded for some $p>1+\frac{2}d$. We prove that the point-to-point partition function can be approximated by two…

Probability · Mathematics 2025-07-03 Stefan Junk

Based on a recently established formalism (U. Ebert, J. Stat. Phys. 82, 183 (1996)) we analyze the diffusive motion of a long polymer in a quenched random medium. The medium is modeled by a frozen semidilute polymer system. In the framework…

Statistical Mechanics · Physics 2015-06-25 Stefan Mueller

In this article, we consider two models of directed polymers in random environment: a discrete model and a continuous model. We consider these models in dimension greater or equal to 3 and we suppose that the normalized partition function…

Probability · Mathematics 2015-06-26 Vincent Vargas

We obtain an exact result for the midpoint probability distribution function (pdf) of the stationary continuum directed polymer, when averaged over the disorder. It is obtained by relating that pdf to the linear response of the stochastic…

Disordered Systems and Neural Networks · Physics 2017-10-09 Christian Maes , Thimothée Thiery

We study the model of Directed Polymers in Random Environment in 1+1 dimensions, where the distribution at a site has a tail which decays regularly polynomially with power \alpha, where \alpha \in (0,2). After proper scaling of temperature…

Probability · Mathematics 2010-01-08 Antonio Auffinger , Oren Louidor

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…

Probability · Mathematics 2007-05-23 Giambattista Giacomin , Fabio Lucio Toninelli

We study the effect of quenched disorder on the zero-range process (ZRP), a system of interacting particles undergoing biased hopping on a one-dimensional periodic lattice, with the disorder entering through random capacities of sites. In…

Statistical Mechanics · Physics 2015-08-04 Shamik Gupta , Mustansir Barma

We consider disordered systems of directed polymer type, for which disorder is so-called marginally relevant. These include the usual (short-range) directed polymer model in dimension (2+1), the long-range directed polymer model with Cauchy…

Probability · Mathematics 2017-01-10 Francesco Caravenna , Rongfeng Sun , Nikos Zygouras

The universality of the directed polymer model and the analogous KPZ equation is supported by numerical simulations using non-Gaussian random probability distributions in two, three and four dimensions. It is shown that although in the…

Disordered Systems and Neural Networks · Physics 2016-08-31 Ehud Perlsman , Shlomo Havlin

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…

Statistical Mechanics · Physics 2016-08-31 Giovanni Sartoni , Attilio L. Stella