Related papers: Universality in marginally relevant disordered sys…
We consider directed polymers in random environment in the critical dimension $d = 2$, focusing on the intermediate disorder regime when the model undergoes a phase transition. We prove that, at criticality, the diffusively rescaled random…
The competition in the pinning of a directed polymer by a columnar pin and a background of random point impurities is investigated systematically using the renormalization group method. With the aid of the mapping to the noisy-Burgers'…
We consider a general model of a disordered copolymer with adsorption. This includes, as particular cases, a generalization of the copolymer at a selective interface introduced by Garel et al. [Europhys. Lett. 8 (1989) 9--13], pinning and…
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…
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…
We study the directed polymer model in a bounded environment with bond disorder and show that, in the interior of the weak disorder phase, weak disorder continues to hold upon perturbation by a small bias. Using this stability result, we…
For the quantum Ising model with ferromagnetic random couplings $J_{i,j}>0$ and random transverse fields $h_i>0$ at zero temperature in finite dimensions $d>1$, we consider the lowest-order contributions in perturbation theory in…
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…
We study the long-range directed polymer model on $\mathbbm{Z}$ in a random environment, where the underlying random walk lies in the domain of attraction of an $\alpha$-stable process for some $\alpha\in(0,2]$. Similar to the more classic…
We elucidate the nature of universal scaling in disordered driven models. We in particularly explore the intriguing possibility of whether coupling with quenched disorders can lead to continuously varying universality classes. We examine…
For a directed polymer model in random environment, a characterization of the weak disorder phase in terms of the moment of the renormalized partition function has been proved in [S. Junk: Communications in Mathematical Physics 389,…
We introduce a new disorder regime for directed polymers in dimension $1+1$ that sits between the weak and strong disorder regimes. We call it the intermediate disorder regime. It is accessed by scaling the inverse temperature parameter…
The equilibrium statistical mechanics of classical directed polymers in 2 dimensions is well known to be equivalent to the imaginary-time quantum dynamics of a 1+1-dimensional many-particle system, with polymer configurations corresponding…
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…
New theoretical and numerical analysis of the one-dimensional contact process with quenched disorder are presented. We derive new scaling relations, different from their counterparts in the pure model, which are valid not only at the…
In this mostly numerical study, we revisit the statistical properties of the ground state of a directed polymer in a $d=1+1$ "hilly" disorder landscape, i.e. when the quenched disorder has power-law tails. When disorder is Gaussian, the…
We consider disordered models of pinning of directed polymers on a defect line, including (1+1)-dimensional interface wetting models, disordered Poland--Scheraga models of DNA denaturation and other (1+d)-dimensional polymers in interaction…
In this paper, we study a disordered pinning model induced by a random walk whose increments have a finite $(2+\kappa)$-th moment for some $\kappa>0$. It is known that this model is marginally relevant, and moreover, it undergoes a phase…
We study the question of how the competition between $\textit{bulk disorder}$ and a $\textit{localized microscopic defect}$ affects the macroscopic behavior of a system in the directed polymer context at the free energy level. We consider…
We construct and study a family random continuum polymer measures $\mathbf{M}_{r}$ corresponding to limiting partition function laws recently derived in a weak-coupling regime of polymer models on hierarchical graphs with marginally…