Related papers: Universality for directed polymers in thin rectang…
The statistics of polymers advected by a turbulent flow are investigated. To limit the polymer lengths above to coil-stretch transition, a FENE-P type relaxation law is used. The turbulence is modeled by a random strain, delta-correlated in…
The first goal of this paper is to prove multiple asymptotic results for a time-discrete and space-continuous polymer model of a random walk in a random potential. These results include: existence of deterministic free energy density in the…
We show that the amplitude of the finite size correction term for the $n$th moment of the partition function, for randomly interacting directed polymers, diverges (on the high temperature side) as $(n_c - n)^{-r}$, as a critical moment…
We study directed polymers subject to a quenched random potential in d transversal dimensions. This system is closely related to the Kardar-Parisi-Zhang equation of nonlinear stochastic growth. By a careful analysis of the perturbation…
In first-passage percolation (FPP), one assigns i.i.d.~weights to the edges of the cubic lattice $\mathbb{Z}^d$ and analyzes the induced weighted graph metric. If $T(x,y)$ is the distance between vertices $x$ and $y$, then a primary…
The author gave the sharp asymptotic behavior of the free energy of $1+1$ dimensional directed polymers in random environment(DPRE) as the inverse temperature $\beta\to 0$ under the assumption that random environment satisfies a certain…
We investigate the nonequilibrium tube length fluctuations during the relaxation of an initially stretched, entangled polymer chain. The time-dependent variance $\sigma^2$ of the tube length follows in the early-time regime a simple…
Half-space directed polymers in random environments are models of interface growth in the presence of an attractive hard wall. They arise naturally in the study of wetting and entropic repulsion phenomena. In 1985, Kardar predicted a…
It has been shown by Pittel and Romik that the random surface associated with a large rectangular Young tableau converges to a deterministic limit. We study the fluctuations from this limit along the edges of the rectangle. We show that in…
For directed polymers, the shape function computes the limiting average energy accrued by paths with a given average slope. We prove that, for a large family of directed polymer models in discrete time and continuous space in dimension…
This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechanical setting, we focus on the low-temperature phases of spin…
The Tracy-Widom distributions are among the most famous laws in probability theory, partly due to their connection with Wigner matrices. In particular, for $A=\frac{1}{\sqrt{n}}(a_{ij})_{1 \leq i,j \leq n} \in \mathbb{R}^{n \times n}$…
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…
Although time-dependent random media with short range correlations lead to (possibly biased) normal tracer diffusion, anomalous fluctuations occur away from the most probable direction. This was pointed out recently in 1D lattice random…
Random percolation can be fully interpreted as a confining pure gauge theory. With numerical high-precision measurements of Polyakov-Polyakov correlators at finite temperature, we could well observe the presence of shape effects due to…
The probability distribution for the number of top to bottom spanning clusters in Directed percolation in two and three dimensions appears to be universal and is of the form $P(n) \sim \exp(-\alpha n^2)$. We argue that $\alpha$ is a new…
The asymptotic analytic expression for the two-time free energy distribution function in (1+1) random directed polymers is derived in the limit when the two times are close to each other
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…
Magnetic field dependent universal conductance fluctuations (UCF's) are observed in weakly disordered indium tin oxide nanowires from 0.26 K up to $\sim 25$ K. The fluctuation magnitudes increase with decreasing temperature, reaching a…
In this paper we consider directed walks on a tree with a fixed branching ratio K at a finite temperature T. We consider the case where each site (or link) is assigned a random energy uncorrelated in time, but correlated in the transverse…