12 citations · 43 across the 12 of their papers we have counts for
15 papers · 1 filter
A sharp asymptotics of the partition function for the collapsed interacting partially directed self-avoiding walk
Alexandre Legrand, Nicolas Pétrélis
In the present paper, we investigate the collapsed phase of the interacting partially-directed self-avoiding walk (IPDSAW) that was introduced in Zwanzig and Lauritzen (1968). We p…
Surface transition in the collapsed phase of a self-interacting walk adsorbed along a hard wall
Alexandre Legrand, Nicolas Pétrélis
The present paper is dedicated to the 2-dimensional Interacting Partially Directed Self Avoiding Walk constrained to remain in the upper-half plan and interacting with the horizont…
Interacting partially directed self-avoiding walk: a probabilistic perspective
Philippe Carmona, Gia Bao Nguyen, Nicolas Pétrélis +1
We review some recent results obtained in the framework of the 2-dimensional Interacting Self-Avoiding Walk (ISAW). After a brief presentation of the rigorous results that have bee…
Limit theorems for Random Walk excursion conditioned to have a typical area
Philippe Carmona, Nicolas Pétrélis
We derive a functional central limit theorem for the excursion of a random walk conditioned on sweeping a prescribed geometric area. We assume that the increments of the random wal…
A shape theorem for the scaling limit of the IPDSAW at criticality
Philippe Carmona, Nicolas Pétrélis
In this paper we give a complete characterization of the scaling limit of the critical Interacting Partially Directed Self-Avoiding Walk (IPDSAW) introduced in Zwanzig and Lauritze…
Scaling limit of the uniform prudent walk
Nicolas Pétrélis, Rongfeng Sun, Niccolò Torri
We study the 2-dimensional uniform prudent self-avoiding walk, which assigns equal probability to all nearest-neighbor self-avoiding paths of a fixed length that respect the pruden…
Collapse transition of the interacting prudent walk
Nicolas Pétrélis, Niccolo Torri
This article is dedicated to the study of the 2-dimensional interacting prudent self-avoiding walk (referred to by the acronym IPSAW) and in particular to its collapse transition.…
Interacting partially directed self avoiding walk : scaling limits
Philippe Carmona, Nicolas Pétrélis
This paper is dedicated to the investigation of a dimensional self-interacting and partially directed self-avoiding walk, usually referred to by the acronym IPDSAW and introd…
Phase diagram for a copolymer in a micro-emulsion
Frank den Hollander, Nicolas Pétrélis
In this paper we study a model describing a copolymer in a micro-emulsion. The copolymer consists of a random concatenation of hydrophobic and hydrophilic monomers, the micro-emuls…
Free energy of a copolymer in a micro-emulsion
Frank den Hollander, Nicolas Pétrélis
In this paper we consider a two-dimensional model of a copolymer consisting of a random concatenation of hydrophilic and hydrophobic monomers, immersed in a micro-emulsion of rando…
Lectures on random polymers
Francesco Caravenna, Frank den Hollander, Nicolas Pétrélis
These lecture notes are a guided tour through the fascinating world of polymer chains interacting with themselves and/or with their environment. The focus is on the mathematical de…
The discrete-time parabolic Anderson model with heavy-tailed potential
Francesco Caravenna, Philippe Carmona, Nicolas Pétrélis
We consider a discrete-time version of the parabolic Anderson model. This may be described as a model for a directed (1+d)-dimensional polymer interacting with a random potential,…
Depinning of a polymer in a multi-interface medium
Francesco Caravenna, Nicolas Pétrélis
In this paper we consider a model which describes a polymer chain interacting with an infinity of equi-spaced linear interfaces. The distance between two consecutive interfaces is…
A polymer in a multi-interface medium
Francesco Caravenna, Nicolas Pétrélis
We consider a model for a polymer chain interacting with a sequence of equispaced flat interfaces through a pinning potential. The intensity of the pinning inter…
Polymer pinning at an interface
Nicolas Pétrélis
In this article, I study the localization transition of an hydrophobic homopolymer in interaction with an interface between oil and water. To that aim I consider a model in which t…