(1) Instituto de F́ısica de Cantabria (UC and CSIC), Avda. de los Castros, s/n, E-39005 Santander, Spain; (2) ICMAT (CSIC-UAM-UC3M-UCM), Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain; (3) Instituto de Investigaciones F́ısicas Mar del Plata (UNMdP and CONICET), Deán Funes 3350, B7602AYL Mar del Plata, Arg...

In this paper we consider, for 1 ≤ m < p < 2, the generalized KPZ equation ut = (u) − |∇u|p. For m = 1, we show existence and uniqueness of the so called very singular solution which is self-similar. A complete classification of self-similar solutions is also given. For m > 1, we establish the existence of very singular self-similar solution and prove that such a solution must have compact supp...

Surface growth governed by the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than two undergoes a roughening transition from smooth to rough phases with increasing nonlinearity. It is also known that KPZ can be mapped onto quantum mechanics of attractive bosons contact interaction, where corresponds binding attraction. Such critical three actually exhibit Efimov effect, three-boson co...

The purpose of this article is to investigate the continuum limit a distributional identity for half-space directed polymers given in [BBC20]. limiting turns out relate multiplicative-noise stochastic heat equation with Dirichlet boundary condition same Robin condition. related conjectured Gaussian fluctuation behavior subcritical KPZ.

Abstract We have analysed the research findings on universality class and discussed connection between Kardar-Parisi-Zhang (KPZ) ballistic deposition model in microscopic rules. In one dimension 1+1 dimensions deviations are not important presence of noise. At same time, they very relevant for higher or deterministic evolution. Mostly, analyses a correction scale than 1280 has been studied yet....

We consider the fluctuation fields of multi-species weakly-asymmetric zero-range interacting particle systems in one dimension, where mass density each species is conserved. Although such have been studied with a single species, setting much less understood. Among other results, we show that when system starts from stationary states particular property, scaling limits fields, seen characteristi...

We consider the stochastic heat equation ∂tZ = ∂ 2 xZ − ZẆ on the real line, where Ẇ is space-time white noise. h(t, x) = − logZ(t, x) is interpreted as a solution of the KPZ equation, and u(t, x) = ∂xh(t, x) as a solution of the stochastic Burgers equation. We take Z(0, x) = exp{B(x)} where B(x) is a two-sided Brownian motion, corresponding to the stationary solution of the stochastic Burgers ...

In this short note, we prove a central limit theorem for type of replica overlap the Brownian directed polymer in Gaussian random environment, low temperature regime and all dimensions. The proof relies on superconcentration result KPZ equation driven by spatially mollified noise, which is inspired recent work Chatterjee [14].