Related papers: Diffusion in planar Liouville quantum gravity
We investigate the application of deformation quantization to the system of a free particle evolving within a universe described by a Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry. This approach allows us to analyze the dynamics of…
For $d > 2$ and $\gamma \in (0, \sqrt{2d})$, we study the Liouville Brownian motion associated with the whole-space log-correlated Gaussian field in $\mathbb{R}^d$. We compute its spectral dimension, i.e., the short-time asymptotics of the…
We investigate anomalous diffusion processes governed by the fractional Langevin equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As the random and damping forces in the fractional Langevin…
Let $\{u(t\,, x)\}_{(t, x)\in \mathbb{R}_+\times \mathbb{R}}$ be the density of one-dimensional super-Brownian motion starting from Lebesgue measure. Using the Laplace functional of super-Brownian motion, we prove that as $N\to \infty$, the…
We study fast / slow systems driven by a fractional Brownian motion $B$ with Hurst parameter $H\in (\frac 13, 1]$. Surprisingly, the slow dynamic converges on suitable timescales to a limiting Markov process and we describe its generator.…
The general covariance of the diffusion equation is exploited in order to explore the curvature effects appearing on brownian motion over a d-dimensional curved manifold. We use the local frame defined by the so called Riemann normal…
Brownian motion in periodic potentials has been widely investigated in statistical physics and related interdisciplinary fields. In the overdamped regime, it has been well-known that the diffusion constant $D^*$ is given by the…
This is the first part of an investigation concerning the formulation of 2D gravity in the framework of the uniformization theory of Riemann surfaces. As a first step in this direction we show that the classical Liouville action appears in…
Realistic dynamical theories of measurement based on the diffusion of quantum states are nonunitary, whereas quantum field theory and its generalizations are unitary. This problem in the quantum field theory of quantum state diffusion (QSD)…
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 invariant metrics. For $\gamma \in (0,2)$ and $\xi =…
We study a relativistic diffusion equation on the Riemannian phase space defined by Franchi and Le Jan. We discuss stochastic Ito (Langevin) differential equations (defining the diffusion) as a perturbation by noise of the geodesic…
The Brownian motion of a test particle interacting with a quantum scalar field in the presence of a perfectly reflecting boundary is studied in (1 + 1)-dimensional flat spacetime. Particularly, the expressions for dispersions in velocity…
We consider the metric growth in Liouville quantum gravity (LQG) for $\gamma \in (0,2)$. We show that a process associated with the trace of the free field on the boundary of a filled LQG ball is stationary, for every $\gamma \in (0,2)$.…
We investigate diffusion-driven flows in a parallel-plate channel domain with linear density stratification, which arise from the combined influence of gravity and diffusion in density-stratified fluids. We compute the time-dependent…
Charged particle beams that remain stationary while passing through a transport channel are represented by ``self-consistent'' phase space distributions. As the starting point, we assume the external focusing forces to act continuously on…
We consider a diffusion process in $\mathbb{R}^d$ with a generator of the form $ L:=\frac 12 e^{V(x)}div(e^{-V(x)}\nabla ) $ where $V$ is measurable and periodic. We only assume that $e^V$ and $e^{-V}$ are locally integrable. We then show…
We construct a planar diffusion process whose infinitesimal generator depends only on the order of the components of the process. Speaking informally and a bit imprecisely for the moment, imagine you run two Brownian-like particles on the…
Active particles self-propel themselves with a stochastically evolving velocity, generating a persistent motion leading to a non-diffusive behavior of the position distribution. Nevertheless, an effective diffusive behavior emerges at times…
We consider the motion of a quantum particle whose position is measured in random places at random moments in time. We show that a freely moving particle measured in this way undergoes superdiffusion, while a charged particle moving in a…
Many important properties of granular fluids can be represented by a system of hard spheres with inelastic collisions. Traditional methods of nonequilibrium statistical mechanics are effective for analysis and description of the inelastic…