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Lorenzo Zambotti

  1. Large deviations for a random speed particle.

    Ср, 03/16/2011 - 16:01 — SomNambul
    Authors: Lorenzo Zambotti, Raphael Lefevere, Mauro Mariani
    Subjects: Probability
    Abstract

    We investigate large deviations for the empirical measure of the position and
    momentum of a particle traveling in a box with hot walls. The particle travels
    with uniform speed from left to right, until it hits the right boundary. Then
    it is absorbed and re-emitted from the left boundary with a new random speed,
    taken from an i.i.d. sequence. It turns out that this simple model, often used
    to simulate a heat bath, displays unusually complex large deviations features,
    that we explain in detail.

  2. Large deviations of the current in stochastic collisional dynamics.

    Пнд, 07/19/2010 - 15:01 — SomNambul
    Authors: Lorenzo Zambotti, Raphael Lefevere, Mauro Mariani
    Subjects: Mathematical Physics
    Abstract

    We consider a class of deterministic local collisional dynamics, showing how
    to approximate them by means of stochastic models and then studying the
    fluctuations of the current of energy. We show first that the variance of the
    time-integrated current is finite and related to the conductivity by the
    Green-Kubo relation. Next we show that the law of the empirical average current
    satisfies a large deviations principle and compute explicitly the rate
    functional in a suitable scaling limit. We observe that this functional is not
    strictly convex.

  3. Uniqueness of post-gelation solutions of a class of coagulation equations.

    Чт, 02/04/2010 - 16:01 — SomNambul
    Authors: Lorenzo Zambotti, Raoul Normand
    Subjects: Classical Analysis and ODEs
    Abstract

    We prove well-posedness of global solutions for a class of coagulation
    equations which exhibit the gelation phase transition. Considering the
    generating functions, we solve an associated partial differential equation
    before and after the phase transition. Applications include the classical
    Smoluchowski and Flory equations with multiplicative coagulation rate and the
    recently introduced symmetric model with limited aggregations.

  4. Approximate maximizers of intricacy functionals.

    Пнд, 09/14/2009 - 09:01 — SomNambul
    Authors: Jerome Buzzi, Lorenzo Zambotti
    Subjects: Probability
    Abstract

    G. Edelman, O. Sporns, and G. Tononi introduced in theoretical biology the
    neural complexity of a family of random variables. This functional is a special
    case of intricacy, i.e., an average of the mutual information of subsystems
    whose weights have good mathematical properties. Moreover, its maximum value
    grows at a definite speed with the size of the system.

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