Related papers: Consecutive Minors for Dyson's Brownian Motions
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
Consider the standard Poisson process in the first quadrant of the Euclidean plane, and for any point (u,v) of this quadrant take the Young diagram obtained by applying the Robinson-Schensted correspondence to the intersection of the…
Recently O'Connell introduced an interacting diffusive particle system in order to study a directed polymer model in 1+1 dimensions. The infinitesimal generator of the process is a harmonic transform of the quantum Toda-lattice Hamiltonian…
We offer an alternative viewpoint on Dyson's original paper regarding the application of Brownian motion to random matrix theory (RMT). In particular we show how one may use the same approach in order to study the stochastic motion in the…
Extended numerical simulations enable to ascertain the diffusive behavior at finite temperatures of chiral walls and skyrmions in ultra-thin model Co layers exhibiting symmetric - Heisenberg - as well as antisymmetric -…
We present equalities in law between the spectra of the minors of a GUE matrix and some maximal functionals of independent Brownian motions. In turn, these results allow to recover the limiting shape (properly centered and scaled) of the…
Brownian motion is modelled by a harmonic oscillator (Brownian particle) interacting with a continuous set of uncoupled harmonic oscillators. The interaction is linear in the coordinates and the momenta. The model has an analytical solution…
The stochastic motion of a particle with long-range correlated increments (the moving phase) which is intermittently interrupted by immobilizations (the traping phase) in a disordered medium is considered in the presence of an external…
We consider a diffusion in $\mathbb{R}^n$ whose coordinates each behave as one-dimensional Brownian motions, that behave independently when apart, but have a sticky interaction when they meet. The diffusion in $\mathbb{R}^n$ can be viewed…
We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding…
In this paper we study the discrete approximation to Brownian motion with varying dimension (BMVD in abbreviation) introduced in [4] by continuous time random walks on square lattices. The state space of BMVD contains a $2$-dimensional…
We consider different Markovian embedding schemes of non-Markovian stochastic processes that are described by generalized Langevin equations (GLE) and obey thermal detailed balance under equilibrium conditions. At thermal equilibrium…
We construct Dyson Brownian motion for $\beta \in (0,\infty]$ by adapting the extrinsic construction of Brownian motion on Riemannian manifolds to the geometry of group orbits within the space of Hermitian matrices. When $\beta$ is…
Based on discrete observations $X_0,X_{\Delta},\dots, X_{n\Delta}$ for $\Delta=n^{-\gamma}$ with $\gamma\in [0,1)$ of the null-recurrent dynamic $dX_t = \sigma(X_t)dW_t$ with a Brownian motion $W$ and $\sigma(x)=\alpha\mathbb{1}\{x<\rho\} +…
The study of spectrum statistics, such as the consecutive-gap ratio distribution, has revealed many interesting properties of many-body complex systems. Here we propose a two-parameter surmise expression for such distribution to describe…
We introduce order-based diffusion processes as the solutions to multidimensional stochastic differential equations, with drift coefficient depending only on the ordering of the coordinates of the process and diffusion matrix proportional…
This work proposes a method for the two-dimensional simulation of Brownian particles in a fluid with restrictions. The method is based on simple numerical rules between two matrices. One of the matrix represent the identification of all…
We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead,…
We establish the representation of general regular diffusions on star-shaped graphs as time-changed Walsh Brownian motions. These are regular continuous Markov processes described locally by a family generalized second order differential…
Discrete diffusion models, like continuous diffusion models, generate high-quality samples by gradually undoing noise applied to datapoints with a Markov process. Gradual generation in theory comes with many conceptual benefits; for…