Alexander Dunlap

activity

20152026

most citedStationary solutions to the stochastic Burgers equation on the line

26 citations · 123 across the 18 of their papers we have counts for

collaborators

Showing math.PRShow all

18 papers · 1 filter

math.PR2026

The Critical 2D KPZ Process

Quentin Berger, Francesco Caravenna, Jeremy Clark +8

This work constructs a non-trivial solution to the ill-defined two-dimensional Kardar-Parisi-Zhang (KPZ) equation at criticality: a distribution-valued stochastic process on the pl…

math.PR2023★ 2 cited

Renormalization flow for the 2D nonlinear stochastic heat equation: pointwise statistics and universality

Alexander Dunlap, Cole Graham

We consider a two-dimensional stochastic heat equation with noise correlated at scale $ρ ≪ 1$ and of strength $∣ lo g ρ ∣^{- 1/2} σ (v)$ depending nonlinearly on the solution $v$ . Under…

math.PR2022★ 3 cited

Localization length of the $1 + 1$ continuum directed random polymer

Alexander Dunlap, Yu Gu, Liying Li

In this paper, we study the localization length of the $1 + 1$ continuum directed polymer, defined as the distance between the endpoints of two paths sampled independently from the q…

math.PR2022★ 3 cited

Invariant measures for stochastic conservation laws on the line

Theodore D. Drivas, Alexander Dunlap, Cole Graham +2

We consider a stochastic conservation law on the line with solution-dependent diffusivity, a super-linear, sub-quadratic Hamiltonian, and smooth, spatially-homogeneous kick-type ra…

math.PR2021★ 9 cited

Fluctuation Exponents of the KPZ equation on a large torus

Alexander Dunlap, Yu Gu, Tomasz Komorowski

We study the one-dimensional KPZ equation on a large torus, started at equilibrium. The main results are optimal variance bounds in the super-relaxation regime and part of the rela…

math.PR2021★ 10 cited

A quenched local limit theorem for stochastic flows

Alexander Dunlap, Yu Gu

We consider a particle undergoing Brownian motion in Euclidean space of any dimension, forced by a Gaussian random velocity field that is white in time and smooth in space. We show…

math.PR2020★ 17 cited

A forward-backward SDE from the 2D nonlinear stochastic heat equation

Alexander Dunlap, Yu Gu

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 $ε > 0$ …

math.PR2020★ 4 cited

Viscous shock solutions to the stochastic Burgers equation

Alexander Dunlap, Lenya Ryzhik

We define a notion of a viscous shock solution of the stochastic Burgers equation that connects "top" and "bottom" spatially stationary solutions of the same equation. Such shocks…

math.PR2020

The continuum parabolic Anderson model with a half-Laplacian and periodic noise

Alexander Dunlap

We construct solutions of a renormalized continuum fractional parabolic Anderson model, formally given by $\partial_{t} u = - (- Δ)^{1/2} u + ξ u$ , where $ξ$ is a periodic spatial white nois…

math.PR2019★ 4 cited

Existence of stationary stochastic Burgers evolutions on $R^{2}$ and $R^{3}$

Alexander Dunlap

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.…

math.PR2019★ 26 cited

Stationary solutions to the stochastic Burgers equation on the line

Alexander Dunlap, Cole Graham, Lenya Ryzhik

We consider invariant measures for the stochastic Burgers equation on $R$ , forced by the derivative of a spacetime-homogeneous Gaussian noise that is white in time and smo…

math.PR2019

Tightness of Liouville first passage percolation for $γ \in (0, 2)$

Jian Ding, Julien Dubédat, Alexander Dunlap +1

We study Liouville first passage percolation metrics associated to a Gaussian free field $h$ mollified by the two-dimensional heat kernel $p_{t}$ in the bulk, and related star-scale…

math.PR2018★ 14 cited

Subsequential scaling limits for Liouville graph distance

Jian Ding, Alexander Dunlap

For $0 < γ < 2$ and $δ > 0$ , we consider the Liouville graph distance, which is the minimal number of Euclidean balls of $γ$ -Liouville quantum gravity measure at most $δ$ whose union con…

math.PR2018

Fluctuations of the solutions to the KPZ equation in dimensions three and higher

Alexander Dunlap, Yu Gu, Lenya Ryzhik +1

We prove, using probabilistic techniques and analysis on the Wiener space, that the large scale fluctuations of the KPZ equation in $d \geq 3$ with a small coupling constant, driven…

math.PR2018

Constructing a solution of the $(2 + 1)$ -dimensional KPZ equation

Sourav Chatterjee, Alexander Dunlap

The $(d + 1)$ -dimensional KPZ equation is the canonical model for the growth of rough $d$ -dimensional random surfaces. A deep mathematical understanding of the KPZ equation for $d = 1$ …

math.PR2018★ 8 cited

The random heat equation in dimensions three and higher: the homogenization viewpoint

Alexander Dunlap, Yu Gu, Lenya Ryzhik +1

We consider the stochastic heat equation $\partial_{s} u = \frac{1}{2} Δ u + (β V (s, y) - λ) u$ , with a smooth space-time stationary Gaussian random field $V (s, y)$ , in dimensions $d \geq 3$ ,…

math.PR2016★ 20 cited

Liouville first-passage percolation: subsequential scaling limits at high temperature

Jian Ding, Alexander Dunlap

Let ${Y_{B} (x) : x \in B}$ be a discrete Gaussian free field in a two-dimensional box $B$ of side length $S$ with Dirichlet boundary conditions.…

math.PR2015★ 1 cited

Expected Regularized Total Variation of Brownian Motion

Alexander Dunlap

We introduce a notion of regularized total variation on an interval for continuous functions with unbounded variation. The definition of regularized total variation is obtained fro…

The Critical 2D KPZ Process

Renormalization flow for the 2D nonlinear stochastic heat equation: pointwise statistics and universality

Localization length of the 1+1 continuum directed random polymer

Invariant measures for stochastic conservation laws on the line

Fluctuation Exponents of the KPZ equation on a large torus

A quenched local limit theorem for stochastic flows

A forward-backward SDE from the 2D nonlinear stochastic heat equation

Viscous shock solutions to the stochastic Burgers equation

The continuum parabolic Anderson model with a half-Laplacian and periodic noise

Existence of stationary stochastic Burgers evolutions on R2 and R3

Stationary solutions to the stochastic Burgers equation on the line

Tightness of Liouville first passage percolation for γ∈(0,2)

Subsequential scaling limits for Liouville graph distance

Fluctuations of the solutions to the KPZ equation in dimensions three and higher

Constructing a solution of the (2+1)-dimensional KPZ equation

The random heat equation in dimensions three and higher: the homogenization viewpoint

Liouville first-passage percolation: subsequential scaling limits at high temperature

Expected Regularized Total Variation of Brownian Motion

Localization length of the $1 + 1$ continuum directed random polymer

Existence of stationary stochastic Burgers evolutions on $R^{2}$ and $R^{3}$

Tightness of Liouville first passage percolation for $γ \in (0, 2)$

Constructing a solution of the $(2 + 1)$ -dimensional KPZ equation