Related papers: KPZ limit theorems
Loop models have been widely studied in physics and mathematics, in problems ranging from polymers to topological quantum computation to Schramm-Loewner evolution. I present new loop models which have critical points described by conformal…
We study the kinetic roughening of the single-step (SS) growth model with a tunable parameter $p$ in $1+1$ and $2+1$ dimensions by performing extensive numerical simulations. We show that there exists a very slow crossover from an…
Depinning of elastic systems advancing on disordered media can usually be described by the quenched Edwards-Wilkinson equation (qEW). However, additional ingredients such as anharmonicity and forces that can not be derived from a potential…
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…
Large scale, dynamical simulations have been performed for the two dimensional octahedron model, describing the Kardar-Parisi-Zhang (KPZ) for nonlinear, or the Edwards-Wilkinson (EW) class for linear surface growth. The autocorrelation…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
The effect of an electric field on conduction in a disordered system is an old but largely unsolved problem. Experiments cover an wide variety of systems - amorphous/doped semiconductors, conducting polymers, organic crystals, manganites,…
In systems where deposition rates are high compared to diffusion, desorption and other mechanisms that generate correlations, a crossover from random to correlated growth of surface roughness is expected at a characteristic time t_0. This…
The decomposition of arbitrary unitary transformations into sequences of simpler, physically realizable operations is a foundational problem in quantum information science, quantum control, and linear optics. We establish a 1D Quantum Field…
Recently we constructed a renormalizable field theory up to two loops for the quasi-static depinning of elastic manifolds in a disordered environment. Here we explore further properties of the theory. We show how higher correlation…
We consider the Cole-Hopf solution of the (1+1)-dimensional KPZ equation started from the narrow wedge initial condition. In this article, we ask how the peaks and valleys of the KPZ height function (centered by time/24) at any spatial…
A universality class describing the statistics of the merging of two single polymer strands to a double polymer strand and the reverse process is examined. The polymers can have an intrinsic direction, and the simpler case, where only…
We analyse scaling laws that govern macromolecules of different topology: polymer chains, homogeneous and miktoarm star polymers in a good solvent possibly constrained by a porous medium. The latter is modelled by long-range-correlated…
Quantum mechanics in a noncommutative plane is considered. For a general two dimensional central field, we find that the theory can be perturbatively solved for large values of the noncommutative parameter ($\theta$) and explicit…
The scaling dimensions of charged operators in conformal field theory have recently been predicted to exhibit universal behavior in the large charge limit. We verify this behavior in the 2+1 dimensional CPN model. Specifically, we…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
We give a general existence result for interacting particle systems with local interactions and bounded jump rates but noncompact state space at each site. We allow for jump events at a site that affect the state of its neighbours. We give…
We study the role of the topology of the background space on the one-dimensional Kardar-Parisi-Zhang (KPZ) universality class. To do so, we study the growth of balls on disordered 2D manifolds with random Riemannian metrics, generated by…
There has been recent interest in new types of topological defects arising in models with compact extra dimensions. We discuss in this context the old statement that if only SU(N) gauge fields and adjoint matter live in the bulk, and the…
It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no mathematical proof of universality and conformal…