Brownian motion is a continuum scaling limit for a wide class of random processes, and
there has been great success in develo** a theory for its properties (such as distribution …

The model of directed polymer in a random environment is a fundamental model of
interaction between a simple random walk and ambient disorder. This interaction gives rise …

We introduce a new concept of solution to the KPZ equation which is shown to extend the
classical Cole-Hopf solution. This notion provides a factorisation of the Cole-Hopf solution …

1. A physical introduction 2 1.1. KPZ/Stochastic Burgers/Scaling exponent 2 1.2. Physical
derivation 3 1.3. Scaling 3 1.4. Formal invariance of Brownian motion 4 1.5. Dynamic scaling …

We introduce what we call the second-order Boltzmann–Gibbs principle, which allows one
to replace local functionals of a conservative, one-dimensional stochastic process by a …

The Kardar–Parisi–Zhang (KPZ) equation is conjectured to universally describe the
fluctuations of weakly asymmetric interface growth. Here we provide the first intrinsic well …

We study a generalized 1d periodic SPDE of Burgers type: ∂ _t u=-A^ θ u+ ∂ _x u^ 2+ A^
θ/2 ξ where θ> 1/2,-A is the 1d Laplacian, ξ is a space–time white noise and the initial …

Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many
such equations are too singular to admit classical treatment. In this article we review some …

We study the stochastic six vertex model and prove that under weak asymmetry scaling (ie,
when the parameter Δ → 1^+ Δ→ 1+ so as to zoom into the ferroelectric/disordered phase …

We consider a class of nearest-neighbor weakly asymmetric mass conservative particle
systems evolving on Z, which includes zero-range and types of exclusion processes, starting …