相关论文: An exact solution for the KPZ equation with flat i…

We compute the pion Generalized Parton Distribution (GPD) in a valence dressed quarks approach. We model the Mellin moments of the GPD using Ans\"atze for Green functions inspired by the numerical solutions of the Dyson-Schwinger Equations…

We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a…

Consider a discrete one-dimensional random surface whose height at a point grows as a function of the heights at neighboring points plus an independent random noise. Assuming that this function is equivariant under constant shifts,…

We study quantitative large-time averages for Hamilton--Jacobi equations in a dynamic random environment that is stationary ergodic and has unit-range dependence in time. Our motivation comes from stochastic growth models related to the…

We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. For totally asymmetric diffusion we calculate the…

We show that under the 1:2:3 scaling, critically probing large space and time, the height function of finite range asymmetric exclusion processes and the KPZ equation converge to the KPZ fixed point, constructed earlier as a limit of the…

Sepp\"al\"ainen and Valk\'o showed in \cite{SV} that for a suitable choice of parameters, the variance growth of the free energy of the stationary O'Connell-Yor polymer is governed by the exponent $2/3$, characteristic of models in the KPZ…

We study the fixed-time spatial covariance of the KPZ equation with flat initial profile. Using Malliavin calculus and a Clark-Ocone representation, we show that as $|x|\to\infty$, $\mathrm{Cov}[h(t,x),h(t,0)]$ is governed by a…

We introduce a simple continuous model for nonequilibrium surface growth. The dynamics of the system is defined by the KPZ equation with a Morse-like potential representing a short range interaction between the surface and the substrate.…

We study the atypically large deviations of the height $H \sim {{\cal O}}(t)$ at the origin at late times in $1+1$-dimensional growth models belonging to the Kardar-Parisi-Zhang (KPZ) universality class. We present exact results for the…

We study the time behavior of the Fokker-Planck equation in Zwanzig rule (the backward-Ito rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in…

We present a new approach to the calculation of thermodynamic functions for crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ Heisemberg chain we derive, for arbitrary values of the anysotropy, a {\bf single}…

We prove existence and uniqueness of distributional solutions to the KPZ equation globally in space and time, with techniques from paracontrolled analysis. Our main tool for extending the analysis on the torus to the full space is a…

We report extensive numerical simulations of growth models belonging to the nonlinear molecular beam epitaxy (nMBE) class, on flat (fixed-size) and expanding substrates (ES). In both $d=1+1$ and $2+1$, we find that growth regime height…

This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…

We report on a new approach to the calculation of thermodynamic functions for crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ Heisenberg chain we derive, for arbitrary values of the anysotropy, a single non-linear…

Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its…

This paper is devoted to the analysis of the large-time behavior of solutions of one-dimensional Fisher-KPP reaction-diffusion equations. The initial conditions are assumed to be globally front-like and to decay at infinity towards the…

We revisit the transfer-matrix approach to directed polymers in random media and show that a single ensemble of random transfer-matrix products provides a unified realization of the canonical one-point fluctuation laws in $(1+1)$…

It is always some constraint that yields any nontrivial structure from statistical averages. As epitomized by the Boltzmann distribution, the energy conservation is often the principal constraint acting on mechanical systems. Here, we…