Dipartimento di Matematica - Universita' di L'Aquila



SEMINARS IN MATHEMATICAL PHYSICS

( Next, Future,Previous)


  • Wednesday: December 5, 2001, 16.30 - ROOM 1.2
    W. OLIVA
    (Universita' tecnica di Lisbona)

    Birkhoff approach to Classical Mechanics


  • Wednesday: December 5, 2001, 17.30 - ROOM 1.2
    Piero NEGRINI
    (Universita' di Roma La Sapienza)

    Sul comportamento asintotico delle soluzioni del problema degli N centri

    Abstract:Il problema degli N centri deve probabilmente la sua popolarita' scientifica al fatto di rappresentare il modello semplificato del problema degli N + 1 corpi ristretto. Si tratta di un punto materiale su varieta 2 o 3 dimensionale, nel campo Newtoniano creato da N centri fissi. Per N = 2, come noto (Eulero) il problema e' integrabile. Per N maggiore od uguale a 3: --Nel caso piano, per livelli di energia positiva e' gia' noto che il sistema non e' integrabile. Voglio presentare nel seminario un risultato ( conseguito con tecniche perturbative) sul comportamento caotico (coniugio con shift di Bernoulli) nel caso di piccole energie negative. --Inoltre, voglio illustrare alcuni recenti risultati (in particolare positivita' della entropia topologica) nel caso di dimensione 3 ed energia positiva. Il punto di partenza e' l'impiego di una tecnica di regolarizzazione che globalizza quella locale di Kunstahiino--Stiefel.












    Previous Seminars.


  • TUESDAY: October 30, 2001, 15.30 - ROOM 0.4
    Angela Stevens
    (Max-Plank Institute for Mathematics in the Sciences Leipzig, Germany)

    Reinforced random walks and their continuous approximations

    Abstract: Global existence and finite time blowup of a PDE-system are discussed, which is formally related to a 1D edge reinforced self attracting random walk. It is shown that the condition for the particle in the random walk to visit a finite number of sites only, is related to the condition for the continuous system to show finite time blowup. Formally vertex reinforced random walks can be approximated by a similar PDE-system. So the results are giving a hint when to expect recurrency in this case and when not.

  • TUESDAY: October 30, 2001, 16.45 - ROOM 0.4
    Roberto Cyril
    (Universita' di Tolosa)

    Path method for the logarithmic Sobolev constant

    Abstract: This talk is concerned with path techniques for quantitative analysis of the logarithmic Sobolev constant on a countable set. We present new upper bounds of the logarithmic Sobolev constant that generalize those given by Sinclair in the case of the spectral gap constant involving path combinatorics. Some examples of applications are given. Then, We compare our bounds to the Hardy constant in the particular case of birth and death processes.
  • WEDNESDAY: October 17, 2001, 17.00 - ROOM 0.4

    NANCY LOPES GARCIA
    (Statistic Department, Campinas University, Brasil)

    Limit behavior of the grain weight in a silo with absorbing walls

    Abstract: We study the nearest neighbors one dimensional uniform q-model of force fluctuations in bead packs [Coppersmith et al (1996)], a stochastic model to simulate the stress of granular media in two dimensional silos. The vertical coordinate plays the role of time, and the horizontal coordinates the role of space. The process is a discrete time Markov process with state space $\R^{\{1,\dots,N\}}$. At each layer (time), the weight supported by each grain is one (its own weight) plus the sum of random fractions of the weights supported by the nearest neighboring grains at the previous layer. The fraction of the weight given to the right neighbor of the successive layer is a uniform random variable in $[0,1]$ independent of everything. The remaining weight is given to the left neighbor. In the boundaries, a uniform fraction of the weight leans on the wall of the silo. This corresponds to \emph{absorbing boundary conditions}. For this model we show that there exists a unique invariant measure. The mean weight at site $i$ under the invariant measure is $i(N+1-i)$; we prove that its variance is $\frac12(i(N+1-i))^2 + O(N^3)$ and the covariances between grains $i\neq j$ are of order $O(N^3)$. Moreover, as $N\to\infty$, the law under the invariant measure of the weights divided by $N^2$ around site (integer part of) $rN$, $r\in (0,1)$, converges to a product of gamma distributions with parameters $2$ and $2(r(1-r))^{-1}$ (sum of two exponentials of mean $r(1-r)/2$). This shows the mean field conjecture of Liu {\it et al} (1995) for this model.

  • THURSDAY: October 4, 2001, 14.30 - ROOM 0.4

    ERWIN BOLTHAUSEN
    (Zurich University)

    A fixed point approach to weakly self-avoiding random walks in dimensions 5 and larger

    Abstract: The law of a self-avoiding random walks of length n is the uniform distribution on the set of nearest-neighbor paths without self-intersections on the hypercubic lattice. A weakly self-avoiding walk suppresses intersections by giving relative weight ( 1-l) Nn to the paths, where Nn is the number of self-intersections, and 0 < l < 1 is a parameter. In a celebrated paper by Brydges and Spencer, it was proved that if the dimension of the lattice is at least 5, then the end-to-end distance scales with Ön and then has asymptotically a Gaussian distribution. The proof of this result was very complicated. The main difficulty is that there is no mass gap. We present a new method which is conceptually very simple, in which is based on a fixed-point argument directly in the space of sequences of distributions. Up to now, the method has only been applied to (weakly) self-avoiding walks, but it should have much wider applications. It also yields stronger pointwise estimates for the two-point functions than those obtained by earlier methods. (This is joint work with Christine Ritzmann)

  • THURSDAY: July 5, 2001, 15.00 - ROOM 0.6

    GEORGE PAPANICOLAU
    (Stanford University)
    MATHEMATICAL BASES FOR IMAGING AND TIME REVERSAL IN RANDOM MEDIA

    Abstract: I will describe briefly the basic phenomena of super-resolution and statistical stability in imaging and time reversal and then I will introduce a framework in stochastic differential equations and flows that can be used to analyze these phenomena.

  • THURSDAY: June 28-2001, 14,30 AULA 04

    Anton Bovier ( Weierstrass Institute for Applied Analysis and Stochastics, Berlino )
    AGING IN THE RANDOM ENERGY MODEL

    Abstract: The concept of "aging" is one of the main paradigms in the theory of the (stochastic) dynamics of disordered systems. In this talk I will show how aging appears in one of the simplest disordered systems, the random energy model. I will briefly review the equilibrium properties of this model, then explain the physical heuristics given by Bouchaud's "REM-like trap model", and finally discuss rigorous results that justify this heuristics.

  • Wednesday: April 11-2001, 14,30 AULA 0.6

    Detlef Durr ( Università di Monaco)
    Probability in Physics

    Abstract: A talk on randomness in physics. Where does randomness come from? The role of typicality.


  • Wednesday: March 14, 2001, 2.30 p.m.,

    Davide Gabrielli ( Università di L'Aquila)

    Fluttuazioni dell'entropia empirica

    Abstract: We will discuss the question of the fluctuations of two estimators of the entropy for a chain with complete connections. We assume that the chain takes values on a finite alphabet and looses memory exponentially fast. We prove a central limit theorem for the conditional entropy of the empirical distribution of the chain, for cylinders growing logarithmically with the length of the sample. We also prove that the entropy of the empirical distribution of the cylinders, divided by the length of the cylinders does not have gaussian fluctuations. The key ingredients of the proofs are an upper bound of the mixing rate of the chain and a regenerative construction of the process.


  • Tuesday: March 27, 2001, 17,00 Room 0.6

    Claudio Landim ( IMPA- Rio de Janeiro, Brazil)

    Convergence to equilibrium of conservative interacting particle systems.


  • Tuesday: April 03, 2001, 17,00 Room 0.6

    Federico Bonetto (Università di Roma, La Sapienza)

    Alcune proprieta' della stato stazionario per il gas di Lorenz periodico con campo elettrico e termostato gaussiano.

    Abstract: Studiamo un sistema di N particelle in un biliardo periodico che si muovono sotto l'azione di un campo elettrico e di un termostato gaussiano che mantiene l'energia cinetica totale costante. Le particelle interagiscono solo attreaverso il termostato. Proponiamo una espressione esplicita per la distribuzione delle velocita' delle particelle quando il campo elettrico e piccolo e la confrontiamo con i dati numerici. Infine discutiamo il limite N->infinito.


  • Wednesday: April 04, 2001, 14,30

    Benedetto Scoppola ( Università di Roma ''La Sapienza'')

    KAC POLYMERS

    Abstract: We show how a random polymer with a stiffness realized > by a Kac potential shows a transition diffusive-ballistic.









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