相关论文: Random polymers via orthogonal Whittaker and sympl…

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…

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…

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,…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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,…