Duerinckx, Mitia Gloria, Antoine
Published in
Annals of PDE

This work is concerned with the mathematical analysis of the bulk rheology of random suspensions of rigid particles settling under gravity in viscous fluids. Each particle generates a fluid flow that in turn acts on other particles and hinders their settling. In an equilibrium perspective, for a given ensemble of particle positions, we analyze both...

Baccelli, François Ramesan, Nithin
Published in
Journal of Mathematical Biology

This paper is focused on SIS (Susceptible-Infected-Susceptible) epidemic dynamics (also known as the contact process) on populations modelled by homogeneous Poisson point processes of the Euclidean plane, where the infection rate of a susceptible individual is proportional to the number of infected individuals in a disc around it. The main focus of...

Motte, Médéric Pham, Huyên

With the emergence of new online channels and information technology, digital advertising tends to substitute more and more to traditional advertising by offering the opportunity to companies to target the consumers/users that are really interested by their products or services. We introduce a novel framework for the study of optimal bidding strate...

Lachièze-Rey, Raphaël

We investigate the zero set of a stationary Gaussian process on the real line, and in particular give lower bounds for the variance of the number of points on a large interval, in all generality. We prove that this point process is never hyperuniform, i.e. the variance is at least linear, and give necessary conditions to have linear variance, which...

Boyer, Alexandre Casse, Jérôme Enriquez, Nathanaël Singh, Arvind

We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model. This class of systems generalizes several classical processes of the same kind, such as Hammersley's broken lin...

BONNET, Anna Dion, Charlotte Gindraud, François Lemler, Sarah

In this work, we propose to catch the complexity of the membrane potential’s dynamic of a motoneuron between its spikes, taking into account the spikes from other neurons around. Our approach relies on two types of data: extracellular recordings of multiple spikes trains and intracellular recordings of the membrane potential of a central neuron. Ou...

huang, lorick Khabou, Mahmoud

Due to its clustering and self-exciting properties, the Hawkes process has been used extensively in numerous fields ranging from sismology to finance. Since data is often aquired on regular time intervals, we propose a piece-wise constant model based on a Discrete-Time Hawkes Process (DTHP). We prove that this discrete-time model converges to the u...

AGATHE-NERINE, Zoé

We consider a population of $N$ interacting neurons, represented by a multivariate Hawkes process : the firing rate of each neuron depends on the history of the connected neurons. Contrary to the mean-field framework where the interaction occurs on the complete graph, the connectivity between particles is given by a random possibly diluted and inho...

Ying, Lexing
Published in
Journal of Scientific Computing

A determinantal point process is a stochastic point process that is commonly used to capture negative correlations. It has become increasingly popular in machine learning in recent years. Sampling a determinantal point process however remains a computationally intensive task. This note introduces a heuristic independent particle approximation to de...

Letendre, Thomas Ueberschär, Henrik

We define a random model for the moments of the new eigenfunctions of a point scat-terer on a 2-dimensional rectangular flat torus. In the deterministic setting,Seba conjectured these moments to be asymptotically Gaussian, in the semi-classical limit. This conjecture was disproved by Kurlberg-Uebersch{\"a}r on Diophantine tori. In our model, we des...