Publications
Non-intersecting Brownian bridges and the Laguerre Orthogonal Ensemble
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Gia Bao Nguyen, Daniel Remenik
Abstract
We show that the squared maximal height of the top path among N non-intersecting Brownian bridges starting and ending at the origin is distributed as the top eigenvalue of a random matrix drawn from the Laguerre Orthogonal Ensemble. This result can be thought of as a discrete version of K. Johansson’s result that the supremum of the Airy2 process minus a parabola has the Tracy-Widom GOE distribution. The result can also be recast in terms of the probability that the top curve of the stationary Dyson Brownian motion hits an hyperbolic cosine barrier.
Quenched invariance principle for random walk in time-dependent balanced random environment
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Jean-Dominique Deuschel, Xiaoqin Guo, Alejandro F. Ramirez
Abstract
We prove a quenched central limit theorem for balanced random walks in time dependent ergodic random environments. We assume that the environment satisfies appropriate ergodicity and ellipticity conditions. The proof is based on the use of a maximum principle for parabolic difference operators.
Ray-Knight representation of flows of branching processes with competition by pruning of Lévy trees
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Julien Berestycki, Maria Clara Fittipaldi, Joaquin Fontbona
Abstract
We introduce the notion of flows of branching processes with competition to describe the evolution of a continuous state branching population in which interactions between individuals give rise to a negative density dependence term. A classical example is the logistic branching processes studied by Lambert. Following the approach developed by Dawson and Li for populations without interactions, such processes are first constructed as the solutions of certain system of stochastic differential equations. We then propose a novel construction of a flow of branching processes with competition based on the interactive pruning of L\’evy-trees, establishing in particular a Ray-Knight representation result for it in terms of the local times of the pruned forest.
Geometric capture and escape of a microswimmer colliding with an obstacle
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Saverio E. Spagnolie, Gregorio R. Moreno-Flores, Denis Bartolo, Eric Lauga
Abstract
Motivated by recent experiments, we consider the hydrodynamic capture of a microswimmer near a stationary spherical obstacle. Simulations of model equations show that a swimmer approaching a small spherical colloid is simply scattered. In contrast, when the colloid is larger than a critical size it acts as a passive trap: the swimmer is hydrodynamically captured along closed trajectories and endlessly orbits around the colloidal sphere. In order to gain physical insight into this hydrodynamic scattering problem, we address it analytically. We provide expressions for the critical trapping radius, the depth of the “basin of attraction,” and the scattering angle, which show excellent agreement with our numerical findings. We also demonstrate and rationalize the strong impact of swimming-flow symmetries on the trapping efficiency. Finally, we give the swimmer an opportunity to escape the colloidal traps by considering the effects of Brownian, or active, diffusion. We show that in some cases the trapping time is governed by an Ornstein-Uhlenbeck process, which results in a trapping time distribution that is well-approximated as inverse-Gaussian. The predictions again compare very favorably with the numerical simulations. We envision applications of the theory to bioremediation, microorganism sorting techniques, and the study of bacterial populations in heterogeneous or porous environments.
Airy processes and variational problems. Chapter in Topics in Percolative and Disordered Systems.
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J. Quastel, D. Remenik.
Abstract
Exact formulas for random growth with half-flat initial data.
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J. Ortmann, J. Quastel, D. Remenik.
Abstract
Renormalization fixed point of the KPZ universality class
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I. Corwin, J. Quastel, D. Remenik.
Abstract
A Pfaffian representation for flat ASEP
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J. Ortmann, J. Quastel, D. Remenik.
Abstract
A classical limit of Noumi’s q-integral operator.
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A. Borodin, I. Corwin, D. Remenik.
Abstract
Robust reconstruction of Barabási-Albert networks in the broadcast congested clique model.
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Pablo Moisset de Espanés, Ivan Rapaport, Daniel Remenik, Javiera Urrutia
Abstract
A variational approach to some transport inequalities
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Joaquin Fontbona, Nathael Gozlan, Jean-Francois Jabir
Abstract
Long time behavior of telegraph processes under convex potentials.
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Joaquin Fontbona, Hélène Guérin, Florent Malrieu
Abstract
Ray-Knight representation of flows of branching processes with competition by pruning of Lévy trees
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Julien Berestycki, Maria Clara Fittipaldi, Joaquin Fontbona
Abstract
Quantitative exponential bounds for the renewal theorem with spread-out distributions
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J.-B Bardet (LMRS), A Christen, J Fontbona (CMM)
Abstract
Quantitative propagation of chaos for generalized Kac particle systems
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Roberto Cortez, Joaquin Fontbona
Abstract
Rate of convergence to equilibrium of fractional driven stochastic differential equations with some multiplicative noise
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Joaquin Fontbona, Fabien Panloup (IMT)
Abstract
Robust utility maximization without model compactness
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Julio Backhoff, Joaquín Fontbona
Abstract
On the long time behavior of stochastic vortices systems
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Joaquin Fontbona, Benjamin Jourdain (INRIA Paris-Rocquencourt, CERMICS)
Abstract
Non local Lotka-Volterra system with cross-diffusion in an heterogeneous medium
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Joaquin Fontbona, Sylvie Méléard
Abstract
A trajectorial interpretation of the dissipations of entropy and Fisher information for stochastic differential equations
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Joaquin Fontbona, Benjamin Jourdain (INRIA Paris-Rocquencourt, CERMICS)
Abstract
Department of Mathematics
Pontifical Catholic University of Chile (PUC-Chile)
Av. Vicuña Mackenna 4860, Macul,
Santiago – Chile
(+56 2) 2354 5779
Center for Mathematical Modeling (CMM)
Faculty of Physical and Mathematical Sciences (FCFM)
Universidad de Chile
Beauchef 851, Edificio Norte, Piso 7,
Santiago – Chile