Related papers: Directed Polymers on Hierarchical Lattices with si…
We study a directed polymer model in a random environment on infinite binary trees. The model is characterized by a phase transition depending on the inverse temperature. We concentrate on the asymptotics of the partition function in the…
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…
We study the force-induced unfolding of a homopolymer on the three dimensional Sierpinski gasket. The polymer is subject to a contact energy between nearest neighbour sites not consecutive along the chain and to a stretching force. The…
Single partially confined collapsed polymers are studied in two dimensions. They are described by self-avoiding random walks with nearest-neighbour attractions below the $\Theta$-point, on the surface of an infinitely long cylinder. For the…
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…
We consider the convergence of partition functions and endpoint density for the half-space directed polymer model in dimension $1+1$ in the intermediate disorder regime as considered for the full space model by Alberts, Khanin and Quastel…
We study numerically the geometrical and free-energy fluctuations of a static one-dimensional (1D) interface with a short-range elasticity, submitted to a quenched random-bond Gaussian disorder of finite correlation length $\xi>0$, and at…
In this article, we present an invariance principle for the paths of the directed random polymer in space dimension two in the subcritical intermediate disorder regime. More precisely, the distribution of diffusively rescaled polymer paths…
We consider a hierarchical model of polymer pinning in presence of quenched disorder, introduced by B. Derrida, V. Hakim and J. Vannimenius in 1992, which can be re-interpreted as an infinite dimensional dynamical system with random initial…
Describing the complex landscape of infinite-dimensional free energy is generally a challenging problem. This difficulty arises from the existence of numerous minimizers and, consequently, a vast number of saddle points. These factors make…
In this article, we derive strong localization results for directed polymers in random environment. We show that at "low temperature" the polymer measure is asymptotically concentrated at a few points of macroscopic mass (we call these…
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…
We consider polarizable sheets modeled by a lattice of delta function potentials. The Casimir interaction of two such lattices is calculated at nonzero temperature. The heat kernel expansion for periodic singular background is discussed in…
A thermo-mechanical continuum theory is proposed for dynamically loaded glassy polymers. The theory is based on an ansatz for the Helmholtz free energy where both the deviatoric and the volumetric contributions to the free energy are…
We consider the behavior of the quantity $p(\beta)$; the free energy of directed polymers in random environment in $1+2$ dimension, where $\beta$ is inverse temperature. We know that the free energy is strictly negative when $\beta$ is not…
The purpose of this paper is to study a one-dimensional polymer penalized by its range and placed in a random environment $\omega$. The law of the simple symmetric random walk up to time $n$ is modified by the exponential of the sum of…
The first part of this paper develops a theory for the free energy of lyotropic polymer nematic liquid crystals. We use a continuum model with macroscopic elastic moduli for a polymer nematic phase. By evaluating the partition function,…
The impact of impenetrable obstacles on the energetics and equilibrium structure of strongly repulsive directed polymers is investigated. As a result of the strong interactions, regions of severe polymer depletion and excess are found in…
We prove that the free energy of the log-gamma polymer between lattice points $(1,1)$ and $(M,N)$ converges to the GUE Tracy-Widom distribution in the $M^{1/3}$ scaling, provided that $N/M$ remains bounded away from zero and infinity. We…
We consider the fluctuations of the free energy of positive temperature directed polymers in thin rectangles (N,N^{\alpha}), \alpha < 3/14. For general weight distributions with finite fourth moment we prove that the distribution of these…