The two-dimensional stochastic heat equation: renormalizing a multiplicative noise

@article{Bertini1998TheTS,
title={The two-dimensional stochastic heat equation: renormalizing a multiplicative noise},
author={Lorenzo Bertini and Nicoletta Cancrini},
journal={Journal of Physics A},
year={1998},
volume={31},
pages={615-622}
}
• Published 16 January 1998
• Mathematics, Physics
• Journal of Physics A
We study, in two space dimensions, the heat equation with a random potential that is a white noise in space and time. We introduce a regularization of the noise and prove that, by a suitable renormalization of the coupling coefficient, the covariance has a non-trivial limit when the regularization is removed. The limit is described in terms of a two-body Schrodinger operator with singular interaction.
• Mathematics
Probability and Mathematical Physics
• 2019
We study the stochastic heat equation in two spatial dimensions with a multiplicative white noise, as the limit of the equation driven by a noise that is mollified in space and white in time. As the
• Mathematics
• 2022
. The critical 2 d Stochastic Heat Flow (SHF) is a stochastic process of random measures on R 2 , recently constructed in [CSZ21]. We show that this process falls outside the class of Gaussian
• Mathematics
Probability Theory and Related Fields
• 2019
We prove, using probabilistic techniques and analysis on the Wiener space, that the large scale fluctuations of the KPZ equation in $$d\ge 3$$ d ≥ 3 with a small coupling constant, driven by a white
• Mathematics
The Annals of Probability
• 2020
We consider the KPZ equation in space dimension 2 driven by space-time white noise. We showed in previous work that if the noise is mollified in space on scale and its strength is scaled as , then a
We prove the two dimensional KPZ equation with a logarithmically tuned nonlinearity and a small coupling constant, scales to the EdwardsWilkinson equation with an effective variance. MSC 2010: 35R60,
• Mathematics
Electronic Journal of Probability
• 2022
. We present a simple criterion, only based on second moment assumptions, for the convergence of polynomial or Wiener chaos to a Gaussian limit. We exploit this criterion to obtain new Gaussian
We prove that the stochastic Burgers equation on R d , d < 4, forced by gradient noise that is white in time and smooth in space, admits spacetime-stationary solutions. These solutions are thus the
• Yu Gu
• Mathematics
Stochastics and Partial Differential Equations: Analysis and Computations
• 2019
We prove the two dimensional KPZ equation with a logarithmically tuned nonlinearity and a small coupling constant, scales to the Edwards–Wilkinson equation with an effective variance.
• Mathematics
The Annals of Probability
• 2022
We consider a nonlinear stochastic heat equation in spatial dimension $d=2$, forced by a white-in-time multiplicative Gaussian noise with spatial correlation length $\varepsilon>0$ but divided by a

References

SHOWING 1-10 OF 14 REFERENCES

• Mathematics, Physics
• 1995
We study, in one space dimension, the heat equation with a random potential that is a white noise in space and time. This equation is a linearized model for the evolution of a scalar field in a
• Mathematics, Physics
• 1995
Abstract We find explicit formulae for the fundamental solution for the heat and time dependent Schrodinger equations with point interaction in dimension n ≤ 3. We discuss in detail the small time
• Physics
Physical review letters
• 1986
A model is proposed for the evolution of the profile of a growing interface that exhibits nontrivial relaxation patterns, and the exact dynamic scaling form obtained for a one-dimensional interface is in excellent agreement with previous numerical simulations.
We study numerically directed polymers in a random potential in 1 + 1 dimensions. We introduce two copies of the polymer, coupled through a thermodynamic local interaction. We show that the system is
• Mathematics
• 1988
We consider a system of random walks or directed polymers interacting weakly with an environment which is random in space and time. In spatial dimensionsd>2, we establish that the behavior is
For every k=1,2,3,...and for a wide class of measures λ, we construct a one-parameter family ℐk(λ, u), u≥0 of functionals of the planar Brownian motion (Xt,Pu) related to its self-intersections of
• Materials Science
Physical review. A, Atomic, molecular, and optical physics
• 1990
We calculate, by performing a product of random matrices, the specific heat and its derivative for the problem of directed polymers in a random medium. Our results are consistent with the existence
• Mathematics
• 1994
En utilisant des techniques de renormalisation de formes quadratiques singulieres, on etudie des Hamiltoniens pour systemes de N particules avec interactions de portee nulle, en dimension deux. Si on
Introduction The one-center point interaction: The one-center point interaction in three dimensions Coulomb plus one-center point interaction in three dimensions The one-center $\delta$-interaction