Rich get richer rule comforts previously often chosen actions. What is happening to the evolution of individual inclinations to choose an action when agents do interact ? Interaction tends to homogenize while each individual dynamics tends to reinforce its own position. Interacting stochastic systems of reinforced processes were recently considered...
We consider the Riemannian random wave model of Gaussian linear combinations of Laplace eigenfunctions on a general compact Riemannian manifold. With probability one with respect to the Gaussian coefficients, we establish that, both for large band and monochro-matic models, the process properly rescaled and evaluated at an independently and uniform...
A continuous-time particle system on the real line verifying the branching property and an exponential integrability condition is called a branching L\'evy process, and its law is characterized by a triplet $(\sigma^2,a,\Lambda)$. We obtain a necessary and sufficient condition for the convergence of the derivative martingale of such a process to a ...
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The first goal of this note is to prove the strong well-posedness of McKean-Vlasov SDEs driven by Lévy processes on $\mathbb{R}^d$ having a finite moment of order $\beta \in [1,2]$ and under standard Lipschitz assumptions on the coefficients. Then, we prove a quantitative propagation of chaos result at the level of paths for the associated interact...
Probabilistic programming languages are used to write probabilistic models to make probabilistic inferences. A number of rigorous semantics have recently been proposed that are now available to carry out formal verification of probabilistic programs. In this paper, we extend an existing formalization of measure and integration theory with s-finite ...
We introduce and compute the generalized disconnection exponents $\eta_\kappa(\beta)$ which depend on $\kappa\in(0,4]$ and another real parameter $\beta$, extending the Brownian disconnection exponents (corresponding to $\kappa=8/3$) computed by Lawler, Schramm and Werner 2001 (conjectured by Duplantier and Kwon 1988). For $\kappa\in(8/3,4]$, the g...
Global sensitivity analysis (GSA) of numerical simulators aims at studying the global impact of the input uncertainties on the output. To perform the GSA, statistical tools based on inputs/output dependence measures are commonly used. We focus here on dependence measures based on reproducing kernel Hilbert spaces: the Hilbert-Schmidt Independence C...
Turbulent cascades characterize the transfer of energy injected by a random force at large scales towards the small scales. In hydrodynamic turbulence, when the Reynolds number is large, the velocity field of the fluid becomes irregular and the rate of energy dissipation remains bounded from below even if the fluid viscosity tends to zero. A mathem...
The Russian airplane crash in 2015 has severely affected the tourism industry in Egypt. The present article is focused on the impacts of economic, political, and social impacts on Egyptian tourism after this crisis. The present study aimed at dealing with the crisis to mitigate the consequences and allow the companies to make the best use of it to ...
