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Exact Solution of Interacting Particle Systems Related to Random Matrices
We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be...
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Piecewise-Tunneled Captive Processes and Corridored Random Particle Systems
We introduce a family of processes that generalises captive diffusions, whereby the stochastic evolution that remains within a pair of time-dependent...
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Twenty-five years of random asset exchange modeling
AbstractThe last 25 years have seen the development of a significant literature within the subfield of econophysics which attempts to model economic...
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Ergodic Theory of Multi-layer Interacting Particle Systems
We consider a class of multi-layer interacting particle systems and characterize the set of ergodic probability measures with finite moments. The...
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Gaussian Fluctuations for Interacting Particle Systems with Singular Kernels
We consider the asymptotic behaviour of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove...
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Stochastic Processes
In this chapter, we lay the foundation of stochastic processes. We start with a general definition of a stochastic process, and then specialize to...
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Derivation of Coupled KPZ Equations from Interacting Diffusions Driven by a Single-Site Potential
The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is derived from various microscopic models, and to...
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Feebly-interacting particles: FIPs 2022 Workshop Report
Particle physics today faces the challenge of explaining the mystery of dark matter, the origin of matter over anti-matter in the Universe, the...
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Some Poisson-Based Processes at Geometric Times
We consider the composition of three different stochastic processes with an independent geometric random time. First, the parent process is assumed...
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Spectral Analysis of Random Networks
We review a general approach that describes the spectra of eigenvalues for random graphs with a local tree-like structure. The exact equations to the...
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Propagation of Chaos for Weakly Interacting Mild Solutions to Stochastic Partial Differential Equations
This article investigates the propagation of chaos property for weakly interacting mild solutions to semilinear stochastic partial differential...
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Resonant Response of Scale-Invariant Functions of a Random Process with a Turbulent Spectrum
AbstractScale-invariant random processes with large fluctuations have been modeled by a system of two stochastic nonlinear differential equations...
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Continuous-Time Random Walks and Temporal Networks
Real-world networks often exhibit complex temporal patterns that affect their dynamics and function. In this chapter, we focus on the mathematical...
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Stochastic approach to evolution of a quantum system interacting with environment in squeezed number state
We determine filtering and master equations for a quantum system interacting with wave packet of light in a continuous-mode squeezed number state. We...
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Krylov complexity and spectral form factor for noisy random matrix models
We study the spectral properties of two classes of random matrix models: non-Gaussian RMT with quartic and sextic potentials, and RMT with Gaussian...
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Derivation of Anomalous Behavior from Interacting Oscillators in the High-Temperature Regime
A microscopic model of interacting oscillators, which admits two conserved quantities, volume, and energy, is investigated. We begin with a system...
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Dynamical Large Deviations for an Inhomogeneous Wave Kinetic Theory: Linear Wave Scattering by a Random Medium
The wave kinetic equation predicts the averaged temporal evolution of a continuous spectral density of waves either randomly interacting or scattered...
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A massive interacting galaxy 510 million years after the Big Bang
James Webb Space Telescope observations have spectroscopically confirmed the existence of galaxies as early as 300 Myr after the Big Bang and with a...
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Dissipative time crystal in a strongly interacting Rydberg gas
The notion of spontaneous symmetry breaking has been well established to characterize classical and quantum phase transitions of matter, such as...
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Random Splitting of Fluid Models: Unique Ergodicity and Convergence
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the...
