Related papers: Point Processes and Multiple SLE/GFF Coupling
We study the local regularity and multifractal nature of the sample paths of jump diffusion processes, which are solutions to a class of stochastic differential equations with jumps. This article extends the recent work of Barral {\it et…
In this note we present new examples of determinantal point processes with infinitely many particles. The particles live on the half-lattice {1,2,...} or on the open half-line (0,+\infty). The main result is the computation of the…
For a broad class of point processes, including determinantal point processes, we construct associated marked and conditional ensembles, which allow to study a random configuration in the point process, based on information about a randomly…
We introduce methods for large scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method at a cost comparable to the…
We investigate collective behavior of a system of two-dimensional interacting Brownian particles in the hydrodynamic regime. By means of the Martin-Siggia-Rose-Jenssen-de Dominicis formalism, we built up a generating functional for…
We consider a random model of diffusion and coagulation. A large number of small particles are randomly scattered at an initial time. Each particle has some integer mass and moves in a Brownian motion whose diffusion rate is determined by…
We consider a system of particles performing a one-dimensional dyadic branching Brownian motion with space-dependent branching rate, negative drift $-\mu$ and killed upon reaching $0$. More precisely, the particles branch at rate…
We study the local statistics of orthogonal polynomial ensembles near a hard edge, subject to a multiplicative deformation of the measure. Probabilistically, this deformation corresponds to a position-dependent conditional thinning of the…
The purpose of the article is twofold. Firstly, we review some recent results on the maximum likelihood estimation in the regression model of the form $X_t = \theta G(t) + B_t$, where $B$ is a Gaussian process, $G(t)$ is a known function,…
We provide an order of convergence for a version of the Carath\'eodory convergence for the multiple SLE model with a Dyson Brownian motion driver towards its hydrodynamic limit, for $\beta=1$ and $\beta=2$. The result is obtained by…
We simulate several models of random curves in the half plane and numerically compute their stochastic driving process (as given by the Loewner equation). Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE)…
We introduce and study a family of random processes with a discrete time related to products of random matrices. Such processes are formed by singular values of random matrix products, and the number of factors in a random matrix product…
We study positive random variables whose moments can be expressed by products and quotients of Gamma functions; this includes many standard distributions. General results are given on existence, series expansion and asymptotics of density…
We develop a Gaussian process framework for learning interaction kernels in multi-species interacting particle systems from trajectory data. Such systems provide a canonical setting for multiscale modeling, where simple microscopic…
Randomized Numerical Linear Algebra (RandNLA) uses randomness to develop improved algorithms for matrix problems that arise in scientific computing, data science, machine learning, etc. Determinantal Point Processes (DPPs), a seemingly…
Consider a system $X = ((x_\xi(t)), \xi \in \Omega_N)_{t \geq 0}$ of interacting Fleming-Viot diffusions with mutation and selection which is a strong Markov process with continuous paths and state space $(\CP(\I))^{\Omega_N}$, where $\I$…
We give a geometric derivation of SLE($\kappa,\rho$) in terms of conformally invariant random growing subsets of polygons. We relate the parameters $\rho_j$ to the exterior angles of the polygons. We also show that SLE($\kappa,\rho$) can be…
Stochastic symmetries and related invariance properties of finite dimensional SDEs driven by general cadlag semimartingales taking values in Lie groups are defined and investigated. The considered set of SDEs, first introduced by S. Cohen,…
We study a stochastic multiscale spatial gene network. These naturally arise in molecular biology. In our model, the reactants are subject to on-site reactions on both scales and diffusion on the continuous scale only, although diffusion on…
It has been proved by Bovier & Hartung [Elect. J. Probab. 19 (2014)] that the maximum of a variable-speed branching Brownian motion (BBM) in the weak correlation regime converges to a randomly shifted Gumbel distribution. The random shift…