Related papers: Localization of directed polymers with general ref…
In this paper we study a two-dimensional directed self-avoiding walk model of a random copolymer in a random emulsion. The copolymer is a random concatenation of monomers of two types, $A$ and $B$, each occurring with density 1/2. The…
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…
We consider large time behavior of typical paths under the Anderson polymer measure. If $P$ is the measure induced by rate $\kappa,$ simple, symmetric random walk on $Z^d$ started at $x,$ this measure is defined as $$ d\mu(X)={Z^{-1}…
We consider the low-temperature $T<T_c$ disorder-dominated phase of the directed polymer in a random potentiel in dimension 1+1 (where $T_c=\infty$) and 1+3 (where $T_c<\infty$). To characterize the localization properties of the polymer of…
We consider directed polymers in a random potential given by a deterministic profile with a strong maximum at the origin taken with random sign at each integer time. We study two main objects based on paths in this random potential. First,…
We analyze a class of continuous time random walks in $\mathbb R^d,d\geq 2,$ with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes…
I discuss models for a continuum directed random polymer in a disordered environment in which the polymer lives on a fractal called the \textit{diamond hierarchical lattice}, a self-similar metric space forming a network of interweaving…
This thesis deals with some $(1+1)$-dimensional lattice path models from the KPZ universality class: the directed random polymer with inverse-gamma weights (known as log-gamma polymer) and its zero temperature degeneration, i.e. the last…
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…
We consider a random walk in a random potential on a square lattice of arbitrary dimension. The potential is a function of an ergodic environment and some steps of the walk. The potential can be unbounded, but it is subject to a moment…
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…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…
We present the exact solutions of various directed walk models of polymers confined to a slit and interacting with the walls of the slit via an attractive potential. We consider three geometric constraints on the ends of the polymer and…
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…
We consider random walk with bounded jumps on a hypercubic lattice of arbitrary dimension in a dynamic random environment. The environment is temporally independent and spatially translation invariant. We study the rate functions of the…
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…
Motivated by renewed interest in the physics of branched polymers, we present here a complete characterization of the connectivity and spatial properties of $2$ and $3$-dimensional single-chain conformations of randomly branching polymers…
Lattice model of directed self avoiding walk is used to investigate adsorption properties of a semiflexible sequential copolymer chain on an impenetrable curved surface on a hexagonal lattice in two dimensions. Walks of the copolymer chains…
We study the localisation of lattice polymer models near a permeable interface in two dimensions. Localisation can arise due to an interaction between the polymer and the interface, and can be altered by a preference for the bulk solvent on…
We consider the model of the directed polymer in a random medium of dimension 1+3, and investigate its multifractal properties at the localization/delocalization transition. In close analogy with models of the quantum Anderson localization…