Related papers: Strong disorder for a certain class of directed po…
An infinite system of point particles placed in $\mathds{R}^d$ is studied. The particles are of two types; they perform random walks in the course of which those of distinct types repel each other. The interaction of this kind induces an…
Forced detachment of a single polymer chain, strongly-adsorbed on a solid substrate, is investigated by two complementary methods: a coarse-grained analytical dynamical model, based on the Onsager stochastic equation, and Molecular Dynamics…
Using a finite size scaling form for reunion probability, we show numerically the existence of a binding-unbinding transition for Directed polymers with random interaction. The cases studied are (A1) two chains in 1+1 dimensions, (A2) two…
We analyze the impact of a porous medium (structural disorder) on the scaling of the partition function of a star polymer immersed in a good solvent. We show that corresponding scaling exponents change if the disorder is…
We study the Busemann process and competition interfaces of the planar directed polymer model with i.i.d.\ weights on the vertices of the planar square lattice, in both the general case and the solvable inverse-gamma case. We prove new…
Cette these est consacree a l' etude de differents modeles aleatoires de polymeres. On s'interesse en particulier a l'influence du desordre sur la localisation des trajectoires pour les modeles d'accrochage et pour les polymeres diriges en…
The first goal of this paper is to prove multiple asymptotic results for a time-discrete and space-continuous polymer model of a random walk in a random potential. These results include: existence of deterministic free energy density in the…
A randomly pinned elastic medium in two dimensions is modeled by a disordered fully-packed loop model. The energetics of disorder-induced dislocations is studied using exact and polynomial algorithms from combinatorial optimization.…
In this note we establish several inequalities and monotonicity properties for the free energy of directed polymers under certain stochastic orders: the usual stochastic order, the Laplace transform order and the convex order. For the…
The way tension propagates along a chain is a key to govern many of anomalous dynamics in macromolecular systems. After introducing the weak and the strong force regimes of the tension propagation, we focus on the latter, in which the…
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…
We prove universality of Tracy-Widom GUE fluctuations for directed polymers in $1+1$ dimensions in the intermediate disorder regime. Building on the Lindeberg replacement method of arXiv:2304.04871, we refine estimates for the measure of…
The overlap of a $d+1$ dimensional directed polymer of length $t$ in a random medium is studied using a Renormalization Group approach. In $d>2$ it vanishes at $T_c$ for $t\rightarrow \infty$ as $t^{\Sigma}$ where…
We study self avoiding random walks in an environment where sites are excluded randomly, in two and three dimensions. For a single polymer chain, we study the statistics of the time averaged monomer density and show that these are well…
We consider a random walk in a random potential, which models a situation of a random polymer and we study the annealed and quenched costs to perform long crossings from a point to a hyperplane. These costs are measured by the so called…
We study the probability that two directed polymers in the same random potential do not intersect. We use the replica method to map the problem onto the attractive Lieb-Liniger model with generalized statistics between particles. We obtain…
We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditions, the solution of this stochastic differential equation…
We consider Markov chains which are polynomially mixing, in a weak sense expressed in terms of the space of functions on which the mixing speed is controlled. In this context, we prove polynomial large and moderate deviations inequalities.…
In this paper, we introduce an index which measures the strength of recurrence of symmetric Markov processes, and give some sufficient conditions for recurrence of direct products of symmetric diffusion processes. The index is given by the…
We revisit the classical problem of the behavior of an isolated linear polymer chain in confined spaces, introducing the distinction between two different confinement regimes (the {\it weak} and the {\it strong} confinement regimes,…