Related papers: A Two-Parameter Family of Infinite-Dimensional Dif…
Despite the simplicity of one-particle dynamics, explicit expressions for the one-dimensional propagator on a circle suitable to numerical evaluation are surprisingly lacking -- not only in the presence of potentials but even in the free…
Forman et al. (2020+) constructed $(\alpha,\theta)$-interval partition evolutions for $\alpha\in(0,1)$ and $\theta\ge 0$, in which the total sums of interval lengths ("total mass") evolve as squared Bessel processes of dimension $2\theta$,…
When the number of particles is finite, the noncolliding Brownian motion (the Dyson model) and the noncolliding squared Bessel process are determinantal diffusion processes for any deterministic initial configuration $\xi=\sum_{j \in…
Strong anomalous diffusion is {often} characterized by a piecewise-linear spectrum of the moments of displacement. The spectrum is characterized by slopes $\xi$ and $\zeta$ for small and large moments, respectively, and by the critical…
We call "Dyson process" any process on ensembles of matrices in which the entries undergo diffusion. We are interested in the distribution of the eigenvalues (or singular values) of such matrices. In the original Dyson process it was the…
The classical model for the genealogies of a neutrally evolving population in a fixed environment is due to Kingman. Kingman's coalescent process, which produces a binary tree, universally emerges from many microscopic models in which the…
Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more…
We discover a deep connection between parity-time (PT) symmetric optical systems and quantum transport in one-dimensional fermionic chains in a two-terminal open system setting. The spectrum of one dimensional tight-binding chain with…
Super-diffusion, characterized by a spreading rate $t^{1/\alpha}$ of the probability density function $p(x,t) = t^{-1/\alpha} p \left( t^{-1/\alpha} x , 1 \right)$, where $t$ is time, may be modeled by space-fractional diffusion equations…
Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive meson electroproduction processes require a generalization of usual parton distributions for the case when long-distance information is accumulated in…
We determine the space-dependent source term for a two-parameter fractional diffusion problem subject to nonlocal non-self-adjoint boundary conditions and two local time-distinct datum. A bi-orthogonal pair of bases is used to construct a…
We show that a slight modification of a theorem of Ruzmaikina and Aizenman on competing particle systems on the real line leads to a characterization of Poisson-Dirichlet distributions $PD(a,0)$. Precisely, let $s$ be a proper random…
Consider an exponential dispersion model (EDM) generated by a probability $ \mu $ on $[0,\infty )$ which is infinitely divisible with an unbounded L\'{e}vy measure $\nu $. The Jorgensen set (i.e., the dispersion parameter space) is then…
The aim of this paper is two-fold: First, we obtain a better understanding of the intrinsic distance of diffusion processes. Precisely, (i) for all $n\ge1$, the diffusion matrix $A$ is weak upper semicontinuous on $\Omega$ if and only if…
The famous Fisher-KPP reaction diffusion model combines linear diffusion with the typical Fisher-KPP reaction term, and appears in a number of relevant applications. It is remarkable as a mathematical model since, in the case of linear…
Let X be the mild solution to a semilinear stochastic partial differential equation. In this article, we develop methodology to sample from the infinite-dimensional diffusion bridge that arises from conditioning X on a linear transformation…
We study the Dyson-Ornstein-Uhlenbeck diffusion process, an evolving gas of interacting particles. Its invariant law is the beta Hermite ensemble of random matrix theory, a non-product log-concave distribution. We explore the convergence to…
In this paper we introduce a new approach to the diffusive limit of the weakly random Schrodinger equation, first studied by L. Erdos, M. Salmhofer, and H.T. Yau. Our approach is based on a wavepacket decomposition of the evolution…
The Thoma simplex $\Omega$ is an infinite-dimensional space, a kind of dual object to the infinite symmetric group. The z-measures are a family of probability measures on $\Omega$ depending on three continuous parameters. One of them is the…
Multitudinous probabilistic and combinatorial objects are associated with generating functions satisfying a composition scheme $F(z)=G(H(z))$. The analysis becomes challenging when this scheme is critical (i.e., $G$ and $H$ are…