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In this paper, we present a new approach to the Kratky-Porod Model (KP) of semiflexible polymers. Our solution to the model is based on the definition of a generating function which we use to study the statistical mechanics of semiflexible…

Statistical Mechanics · Physics 2007-05-23 Marcelo Marucho , Leonardo Loureiro , Gustavo A. Carri

In last passage percolation models lying in the KPZ universality class, the energy of long energy-maximizing paths may be studied as a function of the paths' pair of endpoint locations. Scaled coordinates may be introduced, so that these…

Probability · Mathematics 2019-04-17 Alan Hammond

We study the connection between polymers at the theta temperature on the lattice and Schramm-Loewner chains with constant step length in the continuum. The latter realize a useful algorithm for the exact sampling of tricritical polymers,…

Statistical Mechanics · Physics 2015-06-16 Marco Gherardi

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 earlier work we provided the first evidence that the collapse, or coil-globule, transition of an isolated polymer in solution can be seen in a four-dimensional model. Here we investigate, via Monte Carlo simulations, the canonical…

Statistical Mechanics · Physics 2009-10-31 T. Prellberg , A. L. Owczarek

Motivated by renewed interest in the physics of branched polymers, we present here a complete characterization of the connectivity and spatial properties of $2$ and $3$-dimensional single-chain conformations of randomly branching polymers…

Soft Condensed Matter · Physics 2020-03-23 Irene Adroher-Benítez , Angelo Rosa

In this paper, we discuss possible qualitative approaches to the problem of KPZ universality. Throughout the paper, our point of view is based on the geometrical and dynamical properties of minimisers and shocks forming interlacing…

Mathematical Physics · Physics 2018-03-14 Yuri Bakhtin , Konstantin Khanin

We consider the point-to-point log-gamma polymer of length $2N$ in a half-space with i.i.d. $\operatorname{Gamma}^{-1}(2\theta)$ distributed bulk weights and i.i.d. $\operatorname{Gamma}^{-1}(\alpha+\theta)$ distributed boundary weights for…

Probability · Mathematics 2023-10-17 Guillaume Barraquand , Ivan Corwin , Sayan Das

It has been shown that the last passage time in certain symmetrized models of directed percolation can be written in terms of averages over random matrices from the classical groups $U(l)$, $Sp(2l)$ and $O(l)$. We present a theory of such…

Mathematical Physics · Physics 2015-05-13 Peter J. Forrester , Eric M. Rains

We consider a last passage percolation model in dimension $1+1$ with potential given by the product of a spatial i.i.d. potential with symmetric bounded distribution and an independent i.i.d. in time sequence of signs. We assume that the…

Probability · Mathematics 2025-01-29 Yuri Bakhtin , Konstantin Khanin , András Mészáros , Jeremy Voltz

We prove an identity in distribution between two kinds of partition functions for the log-gamma directed polymer model: (1) the point-to-point partition function in a quadrant, (2) the point-to-line partition function in an octant. As an…

Probability · Mathematics 2022-02-08 Guillaume Barraquand , Shouda Wang

In this note we provide a short proof of the distributional equality between last passage percolation with geometric weights along a general down-right path and Schur processes. We do this in both the full-space and half-space settings, and…

Probability · Mathematics 2025-10-07 Evgeni Dimitrov , Zongrui Yang

A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The…

General Relativity and Quantum Cosmology · Physics 2017-03-31 Hugo A. Morales-Técotl , Saeed Rastgoo , Juan C. Ruelas

We present direct numerical simulations of turbulent channel flow with passive Lagrangian polymers. To understand the polymer behavior we investigate the behavior of infinitesimal line elements and calculate the probability distribution…

Fluid Dynamics · Physics 2013-05-30 Faranggis Bagheri , Dhrubaditya Mitra , Prasad Perlekar , Luca Brandt

We consider the log-Gamma polymer in the half-space with bulk weights distributed as $\operatorname{Gamma}^{-1}(2\theta)$ and diagonal weights as $\operatorname{Gamma}^{-1}(\alpha+\theta)$ for $\theta>0$ and $\alpha>-\theta$. We show that…

Probability · Mathematics 2024-05-09 Sayan Das , Weitao Zhu

Directed paths have been used extensively in the scientific literature as a model of a linear polymer. Such paths models in particular the conformational entropy of a linear polymer and the effects it has on the free energy. These directed…

Soft Condensed Matter · Physics 2015-05-13 E J Janse van Rensburg , T Prellberg , A Rechnitzer

We define the log-gamma sheet and the log-gamma landscape in terms of the 2-parameter and 4-parameter free energy of the log-gamma polymer model and prove that they converge to the Airy sheet and the directed landscape, which are central…

Probability · Mathematics 2025-10-24 Xinyi Zhang

We prove that under n^{1/3} scaling, the limiting distribution as n goes to infinity of the free energy of Seppalainen's log-Gamma discrete directed polymer is GUE Tracy-Widom. The main technical innovation we provide is a general identity…

Probability · Mathematics 2020-10-15 Alexei Borodin , Ivan Corwin , Daniel Remenik

We introduce and study a new model consisting of a single classical random walker undergoing continuous monitoring at rate $\gamma$ on a discrete lattice. Although such a continuous measurement cannot affect physical observables, it has a…

Statistical Mechanics · Physics 2023-01-04 Tony Jin , David G. Martin

The partition function of the directed polymer model on Z^{2+1} undergoes a phase transition in a suitable continuum and weak disorder limit. In this paper, we focus on a window around the critical point. Exploiting local renewal theorems,…

Probability · Mathematics 2019-09-04 Francesco Caravenna , Rongfeng Sun , Nikos Zygouras