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We study a model of directed polymers in random environment in dimension $1+d$, given by a Brownian motion in a Poissonian potential. We study the effect of the density and the strength of inhomogeneities, respectively the intensity…

Probability · Mathematics 2016-01-25 Francis Comets , Nobuo Yoshida

We study asymptotics of the free energy for the directed polymer in random environment. The polymer is allowed to make unbounded jumps and the environment is given by Bernoulli variables. We first establish the existence and continuity of…

Probability · Mathematics 2021-03-03 Francis Comets , Ryoki Fukushima , Shuta Nakajima , Nobuo Yoshida

In these proceedings, we first summarize some general properties of phase transitions in the presence of quenched disorder, with emphasis on the following points: the need to distinguish typical and averaged correlations, the possible…

Disordered Systems and Neural Networks · Physics 2008-03-12 Cecile Monthus , Thomas Garel

We give sharp estimate for the free energy of directed polymers in random environment in dimension 1+1. This estimate was known for a Gaussian environment, we extend it to the case where the law of the environment is infinitely divisible.

Probability · Mathematics 2013-11-25 Frederique Watbled

We study a random walk pinning model, where conditioned on a simple random walk Y on Z^d acting as a random medium, the path measure of a second independent simple random walk X up to time t is Gibbs transformed with Hamiltonian -L_t(X,Y),…

Probability · Mathematics 2009-04-24 Matthias Birkner , Rongfeng Sun

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 present systematic numerical simulations for directed polymers at finite temperatures in 1+1 and 2+1 dimensions. The transverse fluctuations and free energy fluctuations tend to the strong coupling limit at any temperature in both 1+1…

Soft Condensed Matter · Physics 2010-12-07 Xiao-Hong Wang , Shlomo Havlin , Moshe Schwartz

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…

Statistical Mechanics · Physics 2020-05-08 Róbinson J. Acosta Diaz , Christian D. Rodríguez-Camargo , Nami F. Svaiter

This review is devoted to the detailed consideration of the universal statistical properties of one-dimensional directed polymers in a random potential. In terms of the replica Bethe ansatz technique we derive several exact results for…

Statistical Mechanics · Physics 2017-03-14 Victor Dotsenko

For the directed polymer in a random environment (DPRE), two critical inverse-temperatures can be defined. The first one, $\beta_c$, separates the strong disorder regime (in which the normalized partition function $W^{\beta}_n$ tends to…

Probability · Mathematics 2026-04-15 Stefan Junk , Hubert Lacoin

We study the directed polymer model in dimension ${1+1}$ when the environment is heavy-tailed, with a decay exponent $\alpha\in(0,2)$. We give all possible scaling limits of the model in the weak-coupling regime, i.e., when the inverse…

Probability · Mathematics 2018-06-01 Quentin Berger , Niccolo Torri

We study the Cauchy directed polymer model on $\mathbb{Z}^{1+1}$, where the underlying random walk is in the domain of attraction to the $1$-stable law. We show that, if the random walk satisfies certain regularity assumptions and its…

Probability · Mathematics 2018-08-01 Ran Wei

We study an undirected polymer chain living on the 1-dimensional integer lattice and carrying i.i.d.\ random charges. Each self-intersection of the polymer contributes to the Hamiltonian an energy that is equal to the product of the charges…

Probability · Mathematics 2016-03-23 F. Caravenna , F. Den Hollander , N. Pétrélis , J. Poisat

This paper considers an undirected polymer chain on $\mathbb{Z}^d$, $d \geq 2$, with i.i.d.\ random charges attached to its constituent monomers. Each self-intersection of the polymer chain contributes an energy to the interaction…

Mathematical Physics · Physics 2018-02-14 Quentin Berger , Frank den Hollander , Julien Poisat

On the 1+2 dimensional lattice, we consider a directed polymer in a random Gaussian environment that is independent in time and correlated in space. The spatial correlation is supposed to decay as $(\log |x|)^a /|x|^{2}$, $a>-1$, where the…

Probability · Mathematics 2025-10-02 Clément Cosco , Francesca Cottini , Anna Donadini

Zero temperature limit in (1+1) directed polymers with finite range correlated random potential is studied. In terms of the standard replica technique it is demonstrated that in this limit the considered system reveals the one-step replica…

Statistical Mechanics · Physics 2017-02-01 Victor Dotsenko

We study the free energy and its relevant quantity for the directed polymer in random environment. The polymer is allowed to make unbounded jumps and the environment is given by the Bernoulli variables. We first establish the concentration…

Probability · Mathematics 2021-03-26 Shuta Nakajima

We study the critical point of directed pinning/wetting models with quenched disorder. The distribution K(.) of the location of the first contact of the (free) polymer with the defect line is assumed to be of the form…

Probability · Mathematics 2009-11-13 B. Derrida , G. Giacomin , H. Lacoin , F. L. Toninelli

We consider a polymer, with monomer locations modeled by the trajectory of an underlying Markov chain, in the presence of a potential thatinteracts with the polymer when it visits a particular site 0. Disorder is introduced by having the…

Probability · Mathematics 2007-05-23 Kenneth S. Alexander

We consider general disordered models of pinning of directed polymers on a defect line. This class contains in particular the $(1+1)$--dimensional interface wetting model, the disordered Poland--Scheraga model of DNA denaturation and other…

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