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We show that two semi-infinite positive temperature polymers coalesce on the scale predicted by KPZ (Kardar-Parisi-Zhang) universality. The two polymer paths have the same asymptotic direction and evolve in the same environment,…

Probability · Mathematics 2023-05-18 Firas Rassoul-Agha , Timo Seppäläinen , Xiao Shen

The sequence of random probability measures $\nu_n$ that gives a path of length $n$, $\unsur{n}$ times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the…

Probability · Mathematics 2008-08-29 Philippe Carmona

In this paper, we study a model of a Brownian polymer in $\mathbb {R}_+\times \mathbb {R}^d$, introduced by Rovira and Tindel [J. Funct. Anal. 222 (2005) 178--201]. Our investigation focuses mainly on the effect of strong spatial…

Probability · Mathematics 2010-12-10 Hubert Lacoin

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…

Probability · Mathematics 2021-11-23 Jeremy Clark

Limited-valency colloidal particles can self-assemble into polymeric structures analogous to molecules. While their structural equilibrium properties have attracted wide attention, insight into their dynamics has proven challenging. Here,…

Soft Condensed Matter · Physics 2021-09-08 Simon Stuij , Joep Rouwhorst , Hannah Jonas , Nicola Ruffino , Zhe Gong , Stefanno Sacanna , Peter Bolhuis , Peter Schall

In this article we study a \emph{non-directed} polymer model in dimension $d\ge 2$: we consider a simple symmetric random walk on $\mathbb{Z}^d$ which interacts with a random environment, represented by i.i.d. random variables…

Probability · Mathematics 2022-09-26 Quentin Berger , Niccolò Torri , Ran Wei

Recently, nanofluidics experiments have been used to characterize the behavior of single DNA molecules confined to narrow slits etched with arrays of nanopits. Analysis of the experimental data relies on analytical estimates of the…

Soft Condensed Matter · Physics 2024-09-09 James M. Polson , Matthew Kozma

We consider the continuum directed random polymer (CDRP) model that arises as a scaling limit from $1+1$ dimensional directed polymers in the intermediate disorder regime. We show that for a point-to-point polymer of length $t$ and any…

Probability · Mathematics 2022-04-05 Sayan Das , Weitao Zhu

We provide the exact solution of several variants of simple models of the zipping transition of two bound polymers, such as occurs in DNA/RNA, in two and three dimensions using pairs of directed lattice paths. In three dimensions the…

Statistical Mechanics · Physics 2021-02-03 Nicholas R. Beaton , Aleksander L. Owczarek

We consider the behavior of the quantity $p(\beta)$; the free energy of directed polymers in random environment in $1+2$ dimension, where $\beta$ is inverse temperature. We know that the free energy is strictly negative when $\beta$ is not…

Probability · Mathematics 2015-06-22 Makoto Nakashima

Polymers confined in corrugated channels, i.e. channels of varying amplitude, display {multiple local maxima and minima of the diffusion coefficient upon increasing their degree of polymerization $N$}. We propose a theoretical effective…

Soft Condensed Matter · Physics 2023-08-28 Emanuele Locatelli , Valentino Bianco , Chantal Valeriani , Paolo Malgaretti

Consider directed polymers in a random environment on the complete graph of size $N$. This model can be formulated as a product of i.i.d. $N\times N$ random matrices and its large time asymptotics is captured by Lyapunov exponents and the…

Probability · Mathematics 2018-01-22 Francis Comets , Gregorio R. Moreno Flores , Alejandro F. Ramirez

We consider random walk in a space-time random potential, also known as directed random polymer measures, on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices. We construct covariant cocycles…

Probability · Mathematics 2020-06-01 Christopher Janjigian , Firas Rassoul-Agha

This paper is a follow-up work of arxiv.org/abs/2101.05949. We study a non-directed polymer model in random environments. The polymer is represented by a simple symmetric random walk $S$ on $\mathbb{Z}^d$ with $d\geq2$ and the random…

Probability · Mathematics 2025-09-23 Niccolo Torri , Ran Wei

The time-fractional Fokker-Planck equation is a key model for characterizing anomalous diffusion, stochastic transport, and non-equilibrium statistical mechanics with applications in finance, chaotic dynamics, optical physics, and…

Numerical Analysis · Mathematics 2026-01-28 Neetu Garg , Varsha R

The objective of the present paper is to establish exponential large deviation inequalities, and to use them to show exponential concentration inequalities for the free energy of a polymer in general random environment, its rate of…

Probability · Mathematics 2009-09-11 Quansheng Liu , Frédérique Watbled

The aim of this paper is twofold: - To give an elementary and self-contained proof of an explicit formula for the free energy for a general class of polymer chains interacting with an environment through periodic potentials. This…

Probability · Mathematics 2007-05-23 Francesco Caravenna , Giambattista Giacomin , Lorenzo Zambotti

Single partially confined collapsed polymers are studied in two dimensions. They are described by self-avoiding random walks with nearest-neighbour attractions below the $\Theta$-point, on the surface of an infinitely long cylinder. For the…

Statistical Mechanics · Physics 2009-11-07 Hsiao-Ping Hsu , Peter Grassberger

The freely rotating chain is one of the classic discrete models of a polymer in dilute solution. It consists of a broken line of N straight segments of fixed length such that the angle between adjacent segments is constant and the N-1…

Probability · Mathematics 2017-11-15 Philip Kilanowski , Peter March , Marko Samara

We propose and compare different strategies to construct dynamic density functional theories (DDFTs) for inhomogeneous polymer systems close to equilibrium from microscopic simulation trajectories. We focus on the systematic construction of…

Soft Condensed Matter · Physics 2020-09-29 Sriteja Mantha , Shuanhu Qi , Friederike Schmid