Difference between revisions of "Probability Seminar"

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== Fall 2012 ==
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== Spring 2013 ==
  
  
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== Thursday, January 31, Bret Larget, UW-Madison ==
  
== Thursday, September 20, Jun Yin, UW-Madison ==
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Title: TBA
  
Title: Some new results on random matrices.
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Abstract: TBA
  
Abstract:  In this talk, we will introduce some new results on random
 
matrices, especially the necessary and sufficient conditions for universality
 
at the edge and a new result on the circular law.
 
  
== <font color="red">Friday</font>, October 5, Nicos Georgiou, University of Utah ==
 
  
Title: Busemann functions and variational formula for last passage
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==Thursday, March 5, Janosch Ortmann, University of Toronto==
percolation.
 
  
Abstract: Directed last passage percolation on the two dimensional lattice is
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Title: TBA
exactly solvable when the weight distribution is i.i.d. exponential or
 
geometric. The reason for that is the Burke property associated to a model
 
with "boundaries".
 
  
We investigate the solvable model further in order to generalize the idea
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Abstract: TBA
of boundaries into the general setting, and we compute a variational
 
formula for passage times for more general weights. The variatonal formula
 
is given in terms of Busemann functions and all restrictive assumptions on
 
the environment are to guarantee their existence.
 
  
Joint work with T. Seppalainen, F. Rassoul-Agha and A. Yilmaz.
 
  
== Thursday, October 11, No seminar ==
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==Thursday, March 14, Brian Rider, Temple University==
  
because of the MIDWEST PROBABILITY COLLOQUIUM
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Title: TBA
  
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Abstract: TBA
  
== Thursday, October 18, Jason Swanson, University of Central Florida ==
 
  
Title: Correlations within the signed cubic variation of fractional Brownian motion
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==Thursday, March 21, Neil O'Connell, University of Warwick ==
  
Abstract:   The signed cubic variation of the fractional Brownian motion, <math>B</math>, with Hurst parameter <math>H=1/6</math>, is a concept built upon the fact that the sequence, <math>\{W_n\}</math>, of sums of cubes of increments of <math>B</math> converges in law to an independent Brownian motion as the size of the increments tends to zero. In joint work with Chris Burdzy and David Nualart, we study the convergence in law of two subsequences of  <math>\{W_n\}</math>. We prove that, under some conditions on both subsequences, the limit is a two-dimensional Brownian motion whose components may be correlated and we find explicit formulae for its covariance function.
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Title: TBA
  
== Thursday, October 25, Mihai Stoiciu, Williams College ==
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Abstract: TBA
  
Title: Random Matrices with Poisson Eigenvalue Statistics
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== Thursday, April 11, Kevin Lin University of Arizona==
  
Abstract: Several classes of random self-adjoint and random unitary matrices exhibit Poisson microscopic eigenvalue statistics. We will outline the general strategy for proving these results and discuss other models where the Poisson statistics is conjectured. We will also explain how changes in the distribution of the matrix coefficients produce changes in the microscopic eigenvalue distribution and give a transition from Poisson to the picket fence distribution.
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Title: TBA
  
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Abstract: TBA
  
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== Thursday, April 25,  Fraydoun Rezakhanlou, UC - Berkeley==
  
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Title: TBA
  
== Thursday, November 8, Michael Kozdron, University of Regina ==
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Abstract: TBA
  
Title: The Green's function for the radial Schramm-Loewner evolution
 
  
Abstract:  The Schramm-Loewner evolution (SLE), a one-parameter family of random two-dimensional growth processes introduced in 1999 by the late Oded Schramm, has proved to be very useful for studying the scaling limits of discrete models from statistical mechanics. One tool for analyzing SLE itself is the Green's function. An exact formula for the Green's function for chordal SLE was used by Rohde and Schramm (2005) and Beffara (2008) for determining the Hausdorff dimension of the SLE trace. In the present talk, we will discuss the Green's function for radial SLE. Unlike the chordal case, an exact formula is known only when the SLE parameter value is 4. For other values, a formula is available in terms of an expectation with respect to SLE conditioned to go through a point. This talk is based on joint work with Tom Alberts and Greg Lawler.
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== Wednesday, May 1, Bálint Vető, University of Bonn ==
  
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Title: TBA
  
 
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Abstract: TBA
== Thursday, November 15, Gregorio Moreno Flores, University of Wisconsin - Madison ==
 
 
 
Title:  Directed polymers and the stochastic heat equation
 
 
 
Abstract:  We show how some properties of the solutions of the Stochastic Heat Equation (SHE) can be derived from directed polymers in random environment. In particular, we show:
 
* A new proof of the positivity of the solutions of the SHE
 
* Improved bounds on the negative moments of the SHE
 
* Results on the fluctuations of the log of the SHE in equilibrium, namely, the Cole-Hopf solution of the KPZ equation (if time allows).
 
 
 
 
 
== <font color="red">Tuesday</font>, November 27, Michael Damron, Princeton ==
 
 
 
Title: Busemann functions and infinite geodesics in first-passage percolation
 
 
 
Abstract: In first-passage percolation we study the chemical
 
distance in the weighted graph Z^d, where the edge weights are given
 
by a translation-ergodic (typically i.i.d.) distribution. A main open
 
question is to describe the behavior of very long or infinite
 
geodesics. In particular, one would like to know if there are infinite
 
geodesics with asymptotic directions, how many are there, and if
 
infinite geodesics in the same direction coalesce. Some of these
 
questions were addressed in the late 90's by Newman and collaborators
 
under strong assumptions on the limiting shape and weight
 
distribution. I will discuss work with Jack Hanson (Ph. D. student at
 
Princeton) where we develop a framework for working with
 
distributional limits of Busemann functions and use them to prove a
 
form of coalescence of geodesics constructed in any deterministic
 
direction. We also prove existence of infinite geodesics which are
 
asymptotically directed in sectors. Last, we introduce a purely
 
directional condition which replaces Newman's global curvature
 
condition and whose assumption implies the existence of directional
 
geodesics.
 
 
 
 
 
 
 
== Thursday, December 6, Scott McKinley, University of Florida ==
 
 
 
Title: Sensing and Decision-Making in Random Search
 
 
 
Abstract:  Many organisms locate resources in environments in which sensory signals are rare, noisy, and lack directional information. Recent studies of search in such environments model search behavior using random walks (e.g., Levy walks) that match empirical movement distributions. We extend this modeling approach to include searcher responses to noisy sensory data. The results of numerical simulation show that including even a simple response to noisy sensory data can dominate other features of random search, resulting in lower mean search times and decreased risk of long intervals between target encounters. In particular, we show that a lack of signal is not a lack of information. Searchers that receive no signal can quickly abandon target-poor regions. On the other hand, receiving a strong signal leads a searcher to concentrate search effort near targets. These responses cause simulated searchers to exhibit an emergent area-restricted search behavior similar to that observed of many organisms in nature.
 
 
 
 
 
== Thursday, December 13, Karl Liechty, University of Michigan ==
 
 
 
Title:  Extremal statistics of the <math>Airy_2</math> process minus a parabola
 
 
 
Abstract: For a directed polymer in a random medium in the point-to-line geometry, both the fluctuations of the energy and of the position of the polymer can be described in terms of the <math>Airy_2</math> process.  The energy fluctuations are described by the maximum of <math>Airy_2</math> process minus a parabola, and the fluctuations in the location of the endpoint are described by the location of this maximum.  It is known that the maximum of <math>Airy_2</math> process minus a parabola is described by the Tracy-Widom GOE distribution, but somewhat less is known about the location of the maximum.  I will discuss recent work in this area, focusing on the approach to the problem which is based on analysis of orthogonal polynomials.
 

Revision as of 14:35, 22 January 2013


Spring 2013

Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. If you would like to receive announcements about upcoming seminars, please visit this page to sign up for the email list.


Past Seminars

Thursday, September 13, Sebastien Roch, UW-Madison

Title: Markov models on trees: Variants of the reconstruction problem

Abstract: I will consider the so-called `reconstruction problem': how accurately can one guess the state at the root of a Markov chain on a finite tree, given the states at the leaves? I will introduce variants of this problem that arise naturally in connection with applications in molecular evolution, and discuss recent results and open problems. Based on joint works with Andoni, Daskalakis, Hassidim, Mossel and Sly.


Thursday, January 31, Bret Larget, UW-Madison

Title: TBA

Abstract: TBA


Thursday, March 5, Janosch Ortmann, University of Toronto

Title: TBA

Abstract: TBA


Thursday, March 14, Brian Rider, Temple University

Title: TBA

Abstract: TBA


Thursday, March 21, Neil O'Connell, University of Warwick

Title: TBA

Abstract: TBA

Thursday, April 11, Kevin Lin University of Arizona

Title: TBA

Abstract: TBA

Thursday, April 25, Fraydoun Rezakhanlou, UC - Berkeley

Title: TBA

Abstract: TBA


Wednesday, May 1, Bálint Vető, University of Bonn

Title: TBA

Abstract: TBA