Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados

Cost functionals for large random trees

Event Date: Apr 25, 2019 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars, Stochastic Modeling

Abstract : Additive tree functionals allow to represent the cost of many divide-and-conquer algorithms. We give an invariance principle for such tree functionals for the Catalan model and for simply generated trees . In the Catalan model, this relies on the natural embedding into the Brownian excursion.  (Joint work with Jean-François Delmas and Marion Sciauveau)

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Liouville dynamical percolation & The signature method

Event Date: Apr 16, 2019 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars, Stochastic Modeling

Seminario doble conjunto Modelamiento Estocástico / Núcleo Milenio MESCYD Primera Sesión: 3pm Avelio Sepúlveda (U. Lyon 1) Liouville dynamical percolation A dynamical percolation is a process on black and white colourings of the vertices of a graph, in which each vertex has an independent Poissonian clock, and each time a clock rings the colour of its correspondent vertex is resampled. In this talk, we will study a dynamical percolation in the triangular grid, using clocks whose rate is defined in terms of a Liouville measure of parameter $\gamma$. In particular, we will show that this...

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Seminario Conjunto Núcleo MESCD/ Modelamiento Escolástico

Event Date: Dec 04, 2018 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars, Stochastic Modeling

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On Kac’s model, ideal Thermostats, and finite Reservoirs

Event Date: Dec 03, 2018 in CAPDE, Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars

Abstract:   In 1956, Mark Kac introduced a stochastic model to derive a Boltzmann-like equation. Like the space-homogeneous Boltzmann’s  equation, Kac’s equation is ergodic with centered Gaussians as the  unique equilibrium state. In this talk, I will introduce Kac’s model, the thermostat used in [1] to guarantee exponentially fast convergence to equilibrium, and sketch the result in [2] how this infinite  thermostat can be approximated by a finite but large reservoir. References: [1]Bonetto, F., Loss, M.,Vaidyanathan, R.: J. Stat. Phys. 156(4), 647– 667 (2014) [2]Bonetto...

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Seminario Conjunto Núcleo MESCD/ Modelamiento Escolástico

Event Date: Nov 27, 2018 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars, Stochastic Modeling

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Scaling limits for a slowed random walk driven by symmetric exclusion

Event Date: Aug 07, 2018 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars

Abstract: Consider a simple symmetric exclusion process in one dimension, and a random walk on the same space. When on top of particles, the walker has a drift to the left, when on top of holes it has a drift to the right. Under weakly asymmetric scaling, we prove a law of large numbers and a functional central limit theorem for the position of this random walk. The proof uses techniques from the field of hydrodynamic limits to study the fluctuations of the number of particles of the in large boxes around the walker.

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