publication . Article . Other literature type . Preprint . 2018

Interacting partially directed self-avoiding walk: a probabilistic perspective

Philippe Carmona; Gia Bao Nguyen; Nicolas Pétrélis; Niccolò Torri;
Open Access English
  • Published: 01 Jan 2018
  • Publisher: HAL CCSD
  • Country: France
Abstract
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 been obtained so far for ISAW we focus on the Interacting Partially Directed Self-Avoiding Walk (IPDSAW), a model introduced in Zwanzig and Lauritzen (1968) to decrease the mathematical complexity of ISAW. In the first part of the paper, we discuss how a new probabilistic approach based on a random walk representation (see Nguyen and P\'etr\'elis (2013)) allowed for a sharp determination of the asymptotics of the free energy close to criticality (see Carmona, Nguyen and P\'etr\'elis (2016...
Subjects
free text keywords: local limit theorem, Scaling limit, phase transition, Polymer collapse, [MATH]Mathematics [math], [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Mathematics - Probability, Primary 60K35, Secondary 82B26, 82B41, Modelling and Simulation, Statistics and Probability, Mathematical Physics, General Physics and Astronomy, Statistical and Nonlinear Physics, Criticality, Statistical physics, Carmona, biology.organism_classification, biology, Self-avoiding walk, Probabilistic logic, Scaling, Physics, Random walk, Mathematical analysis, Asymptotic analysis
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publication . Article . Other literature type . Preprint . 2018

Interacting partially directed self-avoiding walk: a probabilistic perspective

Philippe Carmona; Gia Bao Nguyen; Nicolas Pétrélis; Niccolò Torri;