Related papers: Stationary measure for the open KPZ equation
In this work, we present sufficient conditions for the existence of a stationary solution of an abstract stochastic Cauchy problem driven by an arbitrary cylindrical L\'evy process, and show that these conditions are also necessary if the…
We study the solution of the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line, equivalently the free energy of the continuum directed polymer in a half space with a…
We study an inhomogeneous Neumann boundary value problem for functions of least gradient on bounded domains in metric spaces that are equipped with a doubling measure and support a Poincar\'e inequality. We show that solutions exist under…
The infinite (in both directions) sequence of the distributions $\mu^{(k)}$ of the stochastic integrals $\int_0^{\infty-}c^{-N_{t-}^{(k)}} dL_t^{(k)}$ for integers $k$ is investigated. Here $c>1$ and $(N_t^{(k)},L_t^{(k)})$, $t\geq0$, is a…
We continue the investigation of limit fluctuations of stationary measures of the asymmetric simple exclusion processes with open boundaries (open ASEP), complementing the recent result by Bryc et al. (2023). It was shown therein that in…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
The first part of the course is devoted to the study of solutions to the Laplace equation in $\Omega\setminus K$, where $\Omega$ is a two-dimensional smooth domain and $K$ is a compact one-dimensional subset of $\Omega$. The solutions are…
We describe a quantum state tomography scheme which is applicable to a system described in a Hilbert space of arbitrary finite dimensionality and is constructed from sequences of two measurements. The scheme consists of measuring the…
We analyze the existence of a parameterized stationary solution $z(\lambda,z_0)=\big(x(\lambda,z_0), p(\lambda,z_0),\,u(\lambda,z_0)\big)\in D\subseteq\mathbb{R}^{2n+1},\,\lambda\in B(0,a)\subseteq\mathop{\prod}\limits_{i=1}^{m}[-a_i,a_i]$,…
We tackle the dynamical description of the quantum measurement process, by explicitly addressing the interaction between the system under investigation with the measurement apparatus, the latter ultimately considered as macroscopic quantum…
This note, dedicated in Harold Widom's memory, is an expanded version of a lecture I gave in fall 2021 at the MSRI program "Universality and Integrability in Random Matrices and Interacting Particle Systems". I will focus on the behavior of…
We show the existence of non-trivial quasi-stationary measures for conservative attractive particle systems on $\ZZ^d$ conditioned on avoiding an increasing local set $\A$. Moreover, we exhibit a sequence of measures $\{\nu_n\}$, whose…
This paper provides a stabilizing preparation method for quantum Gaussian states by utilizing continuous measurement. The stochastic evolution of the open quantum system is described in terms of the quantum stochastic master equation. We…
Given a finite-dimensional real vector space $V$, a probability measure $\mu$ on $\operatorname{PGL}(V)$ and a $\mu$-invariant subspace $W$, under a block-Lyapunov contraction assumption, we prove existence and uniqueness of lifts to…
We consider a family of nonlinear stochastic heat equations of the form $\partial_t u=\mathcal{L}u + \sigma(u)\dot{W}$, where $\dot{W}$ denotes space-time white noise, $\mathcal{L}$ the generator of a symmetric L\'evy process on $\R$, and…
The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is ill-posed because the nonlinearity is marginally defined with respect to the roughness of the forcing noise. However, its Cole-Hopf solution,…
We study the Langevin equation with stationary-increment Gaussian noise. We show the strong consistency and the asymptotic normality with Berry--Esseen bound of the so-called alternative estimator of the mean reversion parameter. The…
The measurement process in quantum mechanics is usually described by the von Neumann projection postulate, which forms a basic constituent of the laws of quantum mechanics. Since this postulate requires the outside observer of the system,…
We study the full Navier--Stokes--Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. The system is supplemented with non-homogeneous Neumann boundary…
In a previous article, given a finite-dimensional real vector space $V$ and a probability measure $\mu$ on $\operatorname{PGL}(V)$ with finite first moment, we gave a description of all $\mu$-stationary probability measures on the…