Related papers: A central limit theorem for two-dimensional direct…
We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…
Motivated by discrete directed polymers in one space and one time dimension, we construct a continuum directed random polymer that is modeled by a continuous path interacting with a space-time white noise. The strength of the interaction is…
We study the collapse of two-dimensional polymers, via an O($n$) model on the square lattice that allows for dilution, bending rigidity and short-range monomer attractions. This model contains two candidates for the theta point,…
We study the central limit theorem for sums of independent tensor powers, $\frac{1}{\sqrt{d}}\sum\limits_{i=1}^d X_i^{\otimes p}$. We focus on the high-dimensional regime where $X_i \in \mathbb{R}^n$ and $n$ may scale with $d$. Our main…
We study energy relaxation in a phenomenological model for polymer built from rheological considerations: a one dimensional nonlinear lattice with dissipative couplings. These couplings are well known in polymer's community to be possibly…
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
We consider Canonical Gibbsian ensembles of Euler point vortices on the 2-dimensional torus or in a bounded domain of R 2 . We prove that under the Central Limit scaling of vortices intensities, and provided that the system has zero global…
A directed polymer is considered on a flat substrate with randomly located parallel ridges. It prefers to lie inside wide regions between the ridges. When the transversel width $W=\exp(\lambda L^{1/3})$ is exponential in the longitudinal…
We present a detailed Monte Carlo study of the high-temperature phase of the two-dimensional driven lattice gas at infinite driving field. We define a finite-volume correlation length, study its finite-size-scaling behavior and extrapolate…
We consider two models for biopolymers, the $\nabla$ interaction and the $\Delta$ one, both with the Gaussian potential in the random environment. A random field $\varphi:{0,1,...,N}\rightarrow \Bbb{R}^d$ represents the position of the…
A directed polymer is allowed to branch, with configurations determined by global energy optimization and disorder. A finite size scaling analysis in 2D shows that, if disorder makes branching more and more favorable, a critical transition…
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…
We study critical spreading dynamics in the two-dimensional contact process (CP) with quenched disorder in the form of random dilution. In the pure model, spreading from a single particle at the critical point $\lambda_c$ is characterized…
The aim of this paper is to investigate the distribution of a continuous homopolymer in the presence of an attractive finitely supported potential. The most intricate behavior can be observed if we simultaneously vary two parameters: the…
We further explore a connection initially unveiled in Iksanov (2025) between critical beta-splitting trees and infinite `balls-in-boxes' schemes. Using the connection, we derive a new joint central limit theorem for components of the height…
The central limit theorem provides the theoretical foundation for the universality of the normal distribution: under broad conditions, the asymptotic distribution of a sum of independent random variables approaches a Gaussian. Yet, physical…
We study the spin n-point functions of the planar Ising model on a simply connected domain \Omega discretised by the square lattice \delta\mathbb{Z}^{2} under near-critical scaling limit. While the scaling limit on the full-plane \mathbb{C}…
In this paper, we derive a central limit theorem for collections of weakly correlated random variables indexed by discrete metric spaces, where the correlation decays in the distance of the indices. The correlation structure we study…
We study a model for a quantum critical point in two spatial dimensions between a semimetallic phase, characterized by a stable quadratic Fermi node, and an ordered phase, in which the spectrum develops a band gap. The quantum critical…
We study a quenched charged-polymer model, introduced by Garel and Orland in 1988, that reproduces the folding/unfolding transition of biopolymers. We prove that, below the critical inverse temperature, the polymer is delocalized in the…