We review and extend recent developments on the statistical properties of Active Ornstein Uhlenbeck particles (AOUPs). In this simplest models, Gaussian white noise overdamped Brownian colloids is replaced by a colored noise. This suffice to grant system hallmark active matter, while still allowing for analytical progress. first detail perturbative derivation steady state AOUPs in small persist...

We study the Dyson–Ornstein–Uhlenbeck diffusion process, an evolving gas of interacting particles. Its invariant law is beta Hermite ensemble random matrix theory, a non-product log-concave distribution. explore convergence to equilibrium this process for various distances or divergences, including total variation, relative entropy, and transportation cost. When number particles sent infinity, ...

We review simple connectionist and firing rate models for mutually inhibiting pools of neurons that discriminate between pairs of stimuli. Both are two-dimensional nonlinear stochastic ordinary differential equations, and although they differ in how inputs and stimuli enter, we show that they are equivalent under state variable and parameter coordinate changes. A key parameter is gain: the maxi...

The discrete Uehling-Uhlenbeck equations are solved to study the propagation of plane (sound) waves in a system of composite fermionic particles with hard-sphere interactions and the filling factor (ν) being 1/2. The Uehling-Uhlenbeck collision sum, as it is highly non-linear, is linearized firstly and then decomposed by using the plane wave assumption. We compare the dispersion relations thus ...

Customers arrive at rate N α on a network of N single server infinite buffer queues, choose L queues uniformly, join the shortest one, and are served there in turn at rate β. We let N go to infinity. We prove a functional central limit theorem (CLT) for the tails of the empirical measures of the queue occupations, in a Hilbert space with the weak topology, with limit given by an Ornstein-Uhlenb...