Seminar on stochastic processes

Members of the probability group are involved in co-organizing remote specialized seminars that take place on Tuesdays and Thursdays:

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Spring Semester 2010

Date / Time Speaker Title Location
24 February 2010
17:15-18:15
Prof. Dr. Michel Emery
Université Louis Pasteur, Strasbourg
Event Details

Seminar on Stochastic Processes

Title A Brownian filtration
Speaker, Affiliation Prof. Dr. Michel Emery, Université Louis Pasteur, Strasbourg
Date, Time 24 February 2010, 17:15-18:15
Location Y27 H 12
Abstract An interesting planar process was described in 1991 by Beneš, Karatzas and Rishel. It turns out that the natural filtration of this process is also generated by some Brownian motion, but the proof is not constructive and we are not able to exhibit any generating BM.
A Brownian filtrationread_more
Y27 H 12
3 March 2010
17:15-18:15
Prof. Dr. Martin Zerner
Universität Tübingen
Event Details

Seminar on Stochastic Processes

Title Interpolation percolation
Speaker, Affiliation Prof. Dr. Martin Zerner, Universität Tübingen
Date, Time 3 March 2010, 17:15-18:15
Location Y27 H 12
Interpolation percolation
Y27 H 12
10 March 2010
17:15-18:14
Prof. Dr. Boguslaw Zegarlinski
Imperial College
Event Details

Seminar on Stochastic Processes

Title Ergodicity of Markov semigroups in Large Dimensions
Speaker, Affiliation Prof. Dr. Boguslaw Zegarlinski, Imperial College
Date, Time 10 March 2010, 17:15-18:14
Location Y27 H 12
Abstract I will talk about ergodicity of nonsymmetric semigroups (with generators having principal part of Hoermander, Levy or Dunkl type) as well as some symmetric semigroups including semigroups on infinite product of Heisenberg groups and / or semigroups with locally conserved quantities.
Ergodicity of Markov semigroups in Large Dimensionsread_more
Y27 H 12
* 24 March 2010
16:15-17:15
Vargas Vincent
Universite Paris Dauphine
Event Details

Seminar on Stochastic Processes

Title Forecasting volatility with the Multifractal Random Walk model
Speaker, Affiliation Vargas Vincent, Universite Paris Dauphine
Date, Time 24 March 2010, 16:15-17:15
Location Y27 H 12
Abstract We study the problem of forecasting volatility for the Multifractal Random Walk (MRW) model. In order to avoid the ill posed problem of estimating the correlation length T of the model, we introduce the infinite range logvolatility as the limit in a quotient space of the MRW logvolatility as T tends to infinity; this infinite range logvolatility is in fact a rigorous formulation of the 1/f noise. For both logvolatilities (infinite range and finite range), we obtain precise prediction formulas and we apply them to the problem of forecasting volatility and pricing options with the MRW model in the absence of a reliable estimate of the average volatility and T.
Forecasting volatility with the Multifractal Random Walk modelread_more
Y27 H 12
* 24 March 2010
17:30-18:30
Atilla Yilmaz
Berkeley
Event Details

Seminar on Stochastic Processes

Title Large deviations for random walk in a random environment
Speaker, Affiliation Atilla Yilmaz , Berkeley
Date, Time 24 March 2010, 17:30-18:30
Location Y27 H 12
Abstract I will talk about large deviations for nearest-neighbor random walk in an i.i.d. environment on $Z^d$. There exist variational formulae for the quenched and the averaged rate functions $I_q$ and $I_a$, obtained by Rosenbluth and Varadhan, respectively. $I_q$ and $I_a$ are not identically equal. However, when $d\geq4$ and the walk satisfies the so-called (T) condition of Sznitman, they are equal on an open set $A_{eq}$. For every $\xi$ in $A_{eq}$, there exists a positive solution to a Laplace-like equation involving $\xi$ and the original transition kernel of the walk. This solution lets us define a new transition kernel via the h-transform technique of Doob. This new kernel corresponds to the unique minimizer of Varadhan's variational formula at $\xi$. It also corresponds to the unique minimizer of Rosenbluth's variational formula provided that the latter is slightly modified. In other words, when the limiting average velocity of the walk is conditioned to be equal to $\xi$, the walk chooses to tilt its original transition kernel by an h-transform.
Large deviations for random walk in a random environmentread_more
Y27 H 12
* 14 April 2010
16:15-17:15
Lorenzo Zambotti
Universite Paris 6
Event Details

Seminar on Stochastic Processes

Title Neural complexity, an entropic functional on families of random variables from theoretical biology
Speaker, Affiliation Lorenzo Zambotti, Universite Paris 6
Date, Time 14 April 2010, 16:15-17:15
Location Y27 H 12
Abstract G. Edelman, O. Sporns and G. Tononi have introduced in theoretical biology the neural complexity of a family of random variables, defining it as a specific average of mutual information over subsystems. We provide a mathematical framework for this concept, studying in particular the problem of maximization of such functional for fixed system size and the asymptotic properties of maximizers as the system size goes to infinity. (Joint work with Jerome Buzzi)
Neural complexity, an entropic functional on families of random variables from theoretical biologyread_more
Y27 H 12
* 14 April 2010
17:30-18:30
Marek Biskup
UCLA
Event Details

Seminar on Stochastic Processes

Title Gibbs distributions on permutations over integers
Speaker, Affiliation Marek Biskup, UCLA
Date, Time 14 April 2010, 17:30-18:30
Location Y27 H 12
Abstract I will discuss a problem that I learned from Daniel Ueltschi some 3 years ago. Consider a probability distribution on the set of all permutations of the integers that weighs a permutation by the exponential of the negative sum of the squares of the displacements between the integers and their images under the permutation. This problem arises as a caricature to Feynman's representation of interacting Bose gases. I will show how to formalize the above description in terms of infinite-volume Gibbs measures and then provide a full classification of all such measures by means of the quantity called a flux. In particular, all Gibbs measures are translation invariant and there is exactly one that has only finite cycles, almost surely. The talk is based on joint work -- and a paper under preparation -- with Thomas Richthammer (UCLA).
Gibbs distributions on permutations over integersread_more
Y27 H 12
* 21 April 2010
16:00-17:00
Philippe Biane
ENS Paris
Event Details

Seminar on Stochastic Processes

Title Scattering for Fourier transforms, orthogonal polynomials and discrete Painleve equations
Speaker, Affiliation Philippe Biane, ENS Paris
Date, Time 21 April 2010, 16:00-17:00
Location Y27 H 12
Scattering for Fourier transforms, orthogonal polynomials and discrete Painleve equations
Y27 H 12
* 21 April 2010
17:30-18:30
Malwina Luczak
London School of Economics
Event Details

Seminar on Stochastic Processes

Title Order-invariant Measures on Causal Sets
Speaker, Affiliation Malwina Luczak, London School of Economics
Date, Time 21 April 2010, 17:30-18:30
Location Y27 H 12
Abstract A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring together two different classes of random processes. In one class, we are given a fixed causal set, and we consider random natural extensions of this causal set: we think of the random enumeration as being generated one point at a time. In the other class of processes, we generate a random causal set, again working from the bottom up, adding one new maximal element at each stage. Processes of both types can exhibit a property called order-invariance: if we stop the process after some fixed number of steps, then, conditioned on the structure of the causal set, every possible order of generation of its elements is equally likely. We develop a framework for the study of order-invariance which includes both types of example: order-invariance is then a property of probability measures on a certain space. Our main result is a description of the extremal order-invariant measures. This is joint work with Graham Brightwell.
Order-invariant Measures on Causal Setsread_more (CANCELLED)
Y27 H 12
28 April 2010
17:15-18:15
Pierre Nolin
Courant Institute
Event Details

Seminar on Stochastic Processes

Title Connection probabilities and RSW-type bounds for the two-dimensional FK Ising model
Speaker, Affiliation Pierre Nolin, Courant Institute
Date, Time 28 April 2010, 17:15-18:15
Location Y27 H 12
Abstract For two-dimensional independent percolation, Russo-Seymour-Welsh (RSW) bounds on crossing probabilities are an important a-priori indication of scale invariance, and they turned out to be instrumental to describe the phase transition. They are in particular a key tool to derive the so-called scaling relations, that link the critical exponents associated with the main macroscopic functions. In this talk, we prove RSW-type uniform bounds on crossing probabilities for the FK Ising model at criticality, independent of the boundary conditions. A central tool in our proof is Smirnov's fermionic observable for the FK Ising model, that makes some harmonicity appear on the discrete level, providing precise estimates on boundary connection probabilities. We also prove several related results - including some new ones - among which the fact that there is no magnetization at criticality, tightness properties for the interfaces, and the value of the half-plane one-arm exponent. This is joint work with H. Duminil-Copin and C. Hongler.
Connection probabilities and RSW-type bounds for the two-dimensional FK Ising modelread_more
Y27 H 12
* 5 May 2010
14:40-18:00
Daniel Hug
Karlsruhe
Leonid Bogachev
Leeds
Ben Hambly
Oxford
Samy Tindel
Nancy
Event Details

Seminar on Stochastic Processes

Title Swiss probability seminar
Speaker, Affiliation Daniel Hug, Karlsruhe
Leonid Bogachev, Leeds
Ben Hambly, Oxford
Samy Tindel, Nancy
Date, Time 5 May 2010, 14:40-18:00
Location Universität Bern, Sidlerstrasse 5, Raum B6
Swiss probability seminar
Universität Bern, Sidlerstrasse 5, Raum B6
12 May 2010
17:15-18:15
Event Details

Seminar on Stochastic Processes

Title No talk
Speaker, Affiliation
Date, Time 12 May 2010, 17:15-18:15
Location Y27 H 12
No talk
Y27 H 12
* 17 May 2010
17:15-18:15
Jason Miller
Stanford University
Event Details

Seminar on Stochastic Processes

Title Universality for SLE(4)
Speaker, Affiliation Jason Miller, Stanford University
Date, Time 17 May 2010, 17:15-18:15
Location Y27 H 12
Abstract We resolve a conjecture of Sheffield that SLE(4), a conformally invariant random curve, is the universal limit of the chordal zero-height contours of random surfaces with isotropic, uniformly convex potentials. Time permitting, we will also explain how the estimates developed for this work can be used to prove a new central limit theorem for linear functionals of such models.
Universality for SLE(4)read_more
Y27 H 12
19 May 2010
17:15-18:15
Event Details

Seminar on Stochastic Processes

Title No talk
Speaker, Affiliation
Date, Time 19 May 2010, 17:15-18:15
Location Y27 H 12
No talk
Y27 H 12
26 May 2010
17:15-18:15
Event Details

Seminar on Stochastic Processes

Title No talk
Speaker, Affiliation
Date, Time 26 May 2010, 17:15-18:15
Location Y27 H 12
No talk
Y27 H 12
2 June 2010
17:15-18:15
David Croydon
University of Warwick
Event Details

Seminar on Stochastic Processes

Title Scaling limit for the random walk on the critical random graph
Speaker, Affiliation David Croydon, University of Warwick
Date, Time 2 June 2010, 17:15-18:15
Location Y27 H 12
Abstract In this talk, a scaling limit for the random walk on the giant component of the critical Erdos-Renyi random graph will be presented. The limiting diffusion is constructed using standard connections between resistance networks and Markov processes, and is shown to share many almost-sure properties with the Brownian motion on Aldous's continuum random tree.
Scaling limit for the random walk on the critical random graphread_more
Y27 H 12

Notes: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location and if you want you can subscribe to the iCal/ics Calender.

Organizers: Andrew Barbour, Erwin Bolthausen, Jiri Cerny, Freddy Delbaen, Ashkan Nikeghbali, Martin Schweizer, Alain-Sol Sznitman

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