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Related papers: Hierarchical pinning model: low disorder relevance…

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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…

Probability · Mathematics 2025-12-23 Ran Wei , Jinjiong Yu

Recent results have lead to substantial progress in understanding the role of disorder in the (de)localization transition of polymer pinning models. Notably, there is an understanding of the crucial issue of disorder relevance and…

Probability · Mathematics 2009-09-24 Giambattista Giacomin , Fabio Lucio Toninelli

Disordered pinning models deal with the (de)localization tran- sition of a polymer in interaction with a heterogeneous interface. In this paper, we focus on two models where the inhomogeneities at the interface are not independent but given…

Probability · Mathematics 2010-12-16 Julien Poisat

We investigate disorder relevance for the pinning of a renewal when the law of the random environment is in the domain of attraction of a stable law with parameter $\gamma \in (1,2)$. Assuming that the renewal jumps have power-law decay, we…

Probability · Mathematics 2016-12-08 Hubert Lacoin

We consider a renewal process \tau={\tau_0,\tau_1,...} on the integers, where the law of \tau_i-\tau_{i-1} has a power-like tail P(\tau_i-\tau_{i-1}=n)=n^{-(\alpha+1)}L(n) with \alpha\ge0 and L(.) slowly varying. We then assign a random,…

Mathematical Physics · Physics 2008-04-28 Fabio Lucio Toninelli

These notes are devoted to the statistical mechanics of directed polymers interacting with one-dimensional spatial defects. We are interested in particular in the situation where frozen disorder is present. These polymer models undergo a…

Probability · Mathematics 2008-06-10 F. Toninelli

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…

Probability · Mathematics 2008-08-22 Fabio Lucio Toninelli

This article investigates the question of disorder relevance for the continuous-time Random Walk Pinning Model (RWPM) and completes the results of our companion paper. The RWPM considers a continuous time random walk $X=(X_t)_{t\geq 0}$,…

Probability · Mathematics 2025-09-11 Quentin Berger , Hubert Lacoin

This paper continues a study initiated in [34], on the localization transition of a lattice free field on $\mathbb Z^d$ interacting with a quenched disordered substrate that acts on the interface when its height is close to zero. The…

Mathematical Physics · Physics 2016-02-17 Hubert Lacoin

We investigate the generalized Poland-Scheraga model, which is used in the bio-physical literature to model the DNA denaturation transition, in the case where the two strands are allowed to be non-complementary (and to have different…

Probability · Mathematics 2018-07-31 Quentin Berger , Giambattista Giacomin , Maha Khatib

We consider the Random Walk Pinning Model studied in [3,2]: this is a random walk X on Z^d, whose law is modified by the exponential of \beta times L_N(X,Y), the collision local time up to time N with the (quenched) trajectory Y of another…

Probability · Mathematics 2010-07-22 Q. Berger , F. Toninelli

A two-dimensional Ising model with short-range interactions and mobile defects describing the formation and thermal destruction of defect stripes is studied. In particular, the effect of a local pinning of the defects at the sites of…

Condensed Matter · Physics 2007-05-23 M. Holtschneider , W. Selke

One dimensional pinning models have been widely studied in the physical and mathematical literature, also in presence of disorder. Roughly speaking, they undergo a transition between a delocalized phase and a localized one. In mathematical…

Mathematical Physics · Physics 2020-12-02 Giambattista Giacomin , Benjamin Havret

As the global HIV pandemic enters its fourth decade, increasing numbers of surveillance sites have been established which allows countries to look into the epidemics at a finer scale, e.g. at sub-national level. However, the epidemic models…

Applications · Statistics 2014-11-18 Le Bao , Mary Mahy , Xiaoyue Niu , Tim Brown , Peter Ghys

We consider wetting of a one-dimensional random walk on a half-line $x\ge 0$ in a short-ranged potential located at the origin $x=0$. We demonstrate explicitly how the presence of a quenched chemical disorder affects the pinning-depinning…

Statistical Mechanics · Physics 2009-11-13 D. M. Gangardt , S. K. Nechaev

A class of discrete renewal processes with super-exponentially decaying inter-arrival distributions coincides with the infinite volume limit of general homogeneous pinning models in their localized phase. Pinning models are statistical…

Probability · Mathematics 2007-06-05 Giambattista Giacomin

We study the dynamics of a viscoelastic medium driven through quenched disorder by expanding about mean field theory in $6-\epsilon$ dimensions. The model exhibits a critical point separating a region where the dynamics is hysteretic with a…

Condensed Matter · Physics 2009-11-07 M. Cristina Marchetti , Karin A. Dahmen

We aim at understanding for which (complex) values of the potential the pinning partition function vanishes. The pinning model is a Gibbs measure based on discrete renewal processes with power law inter-arrival distributions. We obtain some…

Mathematical Physics · Physics 2022-09-01 Giambattista Giacomin , Rafael L. Greenblatt

We address issues related to the presence of defects at finite-temperature topological transitions, in particular when defects are modeled in terms of further variables associated with a quenched disorder, corresponding to the limit in…

Disordered Systems and Neural Networks · Physics 2026-04-20 Claudio Bonati , Ettore Vicari

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