Related papers: Products of Beta matrices and sticky flows
We define a new diffusive matrix model converging towards the $\beta$ -Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the…
This paper aims to provide a simple modelling of speculative bubbles and derive some quantitative properties of its dynamical evolution. Starting from a description of individual speculative behaviours, we build and study a second order…
We use boundary-integral methods to compute the time-dependent deformation of a drop of dielectric fluid immersed in another dielectric fluid in a uniform electric field E. Steady state theory predicts, when the permittivity ratio, \beta,…
Modelling fluid turbulence using a `skeleton' of coherent structures has traditionally progressed by focusing on a few canonical laboratory experiments such as pipe flow and Taylor-Couette flow. We here consider the stratified inclined…
We simulate the two-dimensional XY model in the flow representation by a worm-type algorithm, up to linear system size $L=4096$, and study the geometric properties of the flow configurations. As the coupling strength $K$ increases, we…
We consider several critical wetting models. In the discrete case, these probability laws are known to converge, after an appropriate rescaling, to the law of a reflecting Brownian motion, or of the modulus of a Brownian bridge, according…
We study in some generality intertwinings between $h$-transforms of Karlin-McGregor semigroups associated with one dimensional diffusion processes and those of their Siegmund duals. We obtain couplings so that the corresponding processes…
MeanFlow enables one-step generation in continuous spaces by learning an average velocity over a time interval rather than the instantaneous velocity field of flow matching. However, discrete state spaces do not have smooth trajectories or…
Regime-switching processes contain two components: continuous component and discrete component, which can be used to describe a continuous dynamical system in a random environment. Such processes have many different properties than general…
Qualitative behavior of Bach flow is established on compact four-dimensional locally homogeneous product manifolds. This is achieved by lifting to the homogeneous universal cover and, in most cases, capitalizing on the resultant group…
In this work we connect the theory of Dirichlet forms and direct stochastic calculus to obtain strong existence and pathwise uniqueness for Brownian motion that is perturbed by a series of constant multiples of local times at a sequence of…
The stationary higher-order Markov process for circular data is considered. We employ the mixture transition distribution (MTD) model to express the transition density of the process on the circle. The underlying circular transition…
One-point time-series measurements limit the observation of three-dimensional fully developed turbulence to one dimension. For one-dimensional models, like multiplicative branching processes, this implies that the energy flux from large to…
Bilayer plates are compound materials that exhibit large bending deformations when exposed to environmental changes that lead to different mechanical responses in the involved materials. In this article a new numerical method which is…
Beta-decay and muon-capture experiments in nuclei are reviewed. The conserved vector current hypothesis is confirmed through the observed constancy of the vector coupling constant determined from the superallowed Fermi transitions and from…
Combining a continuous "slab" density with discrete "spike" mass at zero, spike-and-slab priors provide important tools for inducing sparsity and carrying out variable selection in Bayesian models. However, the presence of discrete mass…
We give a Dirichlet form approach for the construction of distorted Brownian motion in a bounded domain $\Omega$ of $\mathbb{R}^d$, $d \geq 1$, with boundary $\Gamma$, where the behavior at the boundary is sticky. The construction covers…
We consider a two-phase Darcy flow in a fractured and deformable porous medium for which the fractures are described as a network of planar surfaces leading to so-called hybrid-dimensional models. The fractures are assumed open and filled…
Directed percolation (DP), a universality class of continuous phase transitions, has recently been established as a possible route to turbulence in subcritical wall-bounded flows. In canonical straight pipe or planar flows, the transition…
In this paper, we introduce and study a unitary matrix-valued process which is closely related to the Hermitian matrix-Jacobi process. It is precisely defined as the product of a deterministic self-adjoint symmetry and a randomly-rotated…