Probability (& Math/Phys) Seminar Schedule
– Fall 2007 –
Previous Seminars
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Speaker:
Title:
Coordinates:
Thomas Richthammer
Department of Mathematics UCLA
The conservation of translational symmetry: Hard-core interaction
(Part II)
Wednesday February 20th
4:00 – 4:50
Location MS–6627
Abstract: One of the main objectives of equilibrium state statistical physics is to analyze and understand the phase portraits of interacting particle systems in equilibrium. In these investigations a crucial task is to study the symmetries of a given system and to see which of them are broken and which of them are conserved. In the seminar I will talk about a fairly general result concerning the conservation of translational symmetry for Gibbsian particle systems in two dimensions, where the interaction is allowed to have a hard core. The presentation will be divided into two parts: The first talk will provide an introduction to the subject and a description of the results, whereas the second talk will focus on the methods used in the proof of the results.
Helen K. Lei
Department of Mathematics UCLA
Conformal Invariance for Certain 2D Percolation Models of the Bond Triangular Type.
Wednesday December 5th
3:00 – 3:50
MS 6229
Abstract: The talk concerns some recent work about bond percolation models on the 2D triangular lattice done in collaboration with I. Binder and L. Chayes. Motivated by a tiling representation of the usual bond percolation problem on the triangular lattice, we construct a one–parameter family of percolation models with local correlations. It is shown that the model possesses the typical attributes which are indicative of critical behavior in 2D percolation systems and, for suitable choice of parameter values, the FKG and BK inequalities are satisfied for path type events. Most importantly, the so called Cardy–Carleson functions are demonstrated to satisfy, in the continuum limit, Cardy’s formula for crossing probabilities. Finally, using all of the above ingredients (and more) convergence to SLE_6 of the percolation exploration process for the model is established. This puts the said model in the same universality class as the standard site percolation model on the triangular lattice (as known from the work of S. Smirnov). The result is proven for a general class of domains: those with boundary (upper) Minkowski dimension less than 2.
Thursday November 29th
3:00 – 3:50
MS 6627
Sebastien Roch
Microsoft Research
Markov Models on Trees: Reconstruction and Applications
Abstract: Markov models on trees arise naturally in many fields of study, notably in Statistical Physics -- as models of evolution; and in Networking -- as models of broadcasting. In this talk, I will consider the so-called ``reconstruction problem'': how accurately can one guess the state at the root of the tree, given the states at the leaves? I will sketch recent work establishing new conditions on the impossibility of such reconstruction. I will also briefly discuss an application of these results to the estimation of evolutionary trees in Biology. This is joint work with Christian Borgs, Jennifer Chayes, and Elchanan Mossel.
Nikolaos Zygouras
Department of Mathematics USC
Pinning-Depinning Transition in Random Polymers.
Wednesday November 7th
3:00 – 3:50
MS 6229
Thomas Richthammer
Department of Mathematics UCLA
Wednesday October 31st,
3:00 – 3:50
MS 6229.
The conservation of translational symmetry: Hard-core interaction
(Part I)
Abstract: One of the main objectives of equilibrium state statistical physics is to analyze and understand the phase portraits of interacting particle systems in equilibrium. In these investigations a crucial task is to study the symmetries of a given system and to see which of them are broken and which of them are conserved. In the seminar I will talk about a fairly general result concerning the conservation of translational symmetry for Gibbsian particle systems in two dimensions, where the interaction is allowed to have a hard core. The presentation will be divided into two parts: The first talk will provide an introduction to the subject and a description of the results, whereas the second talk will focus on the methods used in the proof of the results.
Wednesday October 17th,
3:00 – 3:50
MS 6229.
Thomas M. Liggett
Department of Mathematics UCLA
Negative Dependence and the Symmetric Exclusion Process
Abstract: Over the past several years, several conjectures related to negative dependence of Bernoulli random variables have been made. Among them are: (a) the Rayleigh property (also known as the hereditary negative lattice condition after application of (external fields) implies the ultra logconcavity (ULC) of the rank sequence, (b) the Rayleigh property implies negative association, and (c) the symmetric exclusion process with product initial distribution is negatively associated at positive times. We will discuss these and other conjectures. Among the results: (a) is false and (c) is true, while (b) is still open. Furthermore, a stronger form of the Rayleigh property does imply both ULC and negative association. As a consequence of (c), we obtain distributional limit theorems for certain functionals of the symmetric exclusion process. Much of this is joint work with J. Borcea and P. Branden.
Ilia Binder
Department of Mathematics University of Toronto
Geometric Properties of the
Stochastic Löewner Evolution
Wednesday October 10th,
3:00 – 3:50
MS 6229.
Abstract: I will talk about certain geometric properties of the typical trajectories of the Stochastic Loewner Evolution (SLE). I will discuss the problem of the behavior of the $SLE_\kappa$ trajectory for a typical driving force and varying $\kappa$. I will also describe the multifractal spectrum of the harmonic measure and the local winding.
Pietro Caputo
On the Approach to Equilibrium for a Polymer with Adsorption and Repulsion
Thursday October 4th,
3:00 – 3:50
MS 6627.
Dipartimento di Matematica, Università Roma Tre
Abstract: We study the decay to equilibrium of a Glauber dynamics for a polymer pinning model. We derive several estimates on relaxation time and mixing time of the process which illustrate the well known localization/delocalization transition from a dynamical point of view. Some open problems are also discussed. This is joint work with Fabio Martinelli and Fabio Lucio Toninelli.