Department of Mathematics

Wednesdays

Carver 202
1:10 to 2:00 p.m.

 

For more information, contact:

Krishna Athreya
kba@iastate.edu
515-294-5864 (Math)
515-294-2617 (Stat)

Probability Seminar

Spring 2009

 

May 6

Krishna Athreya will present, Limit theorems for Gibbs measures.

 

April 29

Krishna Athreya will present

 

April 15

Krishna Athreya will present, Convergence of Gibbs measures and Laplace's method.

February 25

Viatcheslav Dobrovitski (Ames Labs and Physics Dept.) on Measurement of quantum systems: Bayesian inference and state estimation

 

February 18

Ryan Martin on Tight concentration of graph parameters and applications

 

February 4

Discussion of open questions about simple random walk on Z.  Surprisingly, there are still a number of easy-to-formulate and innocent- looking unsolved problems about simple random walk.  This discussion will be predominantly based on the paper by Zhan Shi and Balint Toth entitled Favorite Sites of Simple Random Walk]. Alex Roitershtein will begin the discussion.

January 28

Ananda Weerasinghe on Solvable stochastic control problems

 

Fall 2008

November 12

Vivek Roy
Haggstrom and Rosenthal's Variance condition for Markov Chain CLT

 

November 5

Steve Willson
Using Markov models on trees to reconstruct evolutionary history

October 22

Vivek Roy (Statistics)
Convergence rates for MCMC algorithms for Bayesian multivariate Student's t regression

We'll discuss the importance of  rigorous analysis of convergence rates of Markov chains underlying MCMC algorithms in general. As an example, we'll consider multivariate regression models where the distribution of the error variable is a multivariate Student's $t$ distribution.

We'll develop and compare two Markov chain Monte Carlo algorithms, namely a Data augmentation (DA) algorithm and a Haar PX-DA algorithm for exploring the posterior distribution that results when the above regression model is combined with the standard non-informative prior. We'll prove that, under certain conditions, both of these algorithms converge at a geometric rate.

October 15

Ananda Weerasinghe
Optimal control of a stochastic network driven by fractional Brownian motion input (continued)

October 1

Ananda Weerasinghe
Optimal control of a stochastic network driven by fractional Brownian motion input

September 17

Alex Roiterstein
Random walks on Z in a cookie environment (continued)

September 10

Alex Roiterstein
Random walks on Z in a cookie environment

So called excited random walk, or random walks in a cookie environment, have attracted much attention over the last years. These are self-interacting random walks traveling on a lattice with a number of "cookies" put in advance in each site. Roughly, when the walker meets a cookie, eats it, gets excited, and then change his behavior (transition kernel) for just the next jump. Once there is no more cookie in a site, the random walk arriving there behaves like the ordinary symmetric random walk, that is chooses each direction with equal probabilities. I will survey some recent results about these random walks in dimension one.

September 3

Sunder Sethuraman
Large deviations for some urn and random graph models (continued)

August 27

Sunder Sethuraman
Large deviations for some urn and random graph models

 

Spring 2008

March 26

Alex Roitershtein
Random walkin random environments

March 12

Alex Roitershtein
Multiple points for random walk in random environments

February 19

Ananda Weerasinghe
Fractional Brownian motion (continued)

February 12

Ananda Weerasinghe
Fractional Brownian motion

January 23

Ananda Weerasinghe
Limit theorems for one funcionals of one dim SBM

 

Fall 2007

November 15 (Note different day/time) from 11:00 a.m. to 11:50 a.m. in 390 Carver

Speaker - Jonathon Peterson, University of Minnesota

Quenched limits for transient one-dimensional random walks in a random environment

For a transient, one-dimensional random walk in random environment, Kesten, Kozlov, and Spitzer ('75) proved that the annealed limiting distribution of the random walk was related to a stable distribution. We instead study the quenched behavior of the random walk and show that there are no quenched limiting distributions for the random walk. In particular, in the positive speed regime we can find two random subsequences (depending on the environment) along which the limiting distribution of the random walk is either a Gaussian or a reverse exponential distribution.

November 7

Speaker - Mathieu Merle, University of British Columbia

The continuous limit of invasion percolation on a regular tree

We consider invasion percolation on a regular tree. Recent work of Angel, Goodman, den Hollander and Slade showed a structural representation of the invasion percolation cluster (IPC) as an infinite backbone from which emerge independent sub-critical Galton-Watson trees.

This representation allows a better understanding of the similarities and differences between (IPC) and incipient infinite cluster on a regular tree.

We use this structural representation to show that the (IPC), when suitably rescaled, converges to a continuous tree. The limit can be used to deduce asymptotic properties of the (IPC).
This is joint work with Omer Angel (U of Toronto) and Jesse Goodman (UBC).

October 24

Speaker - Alexander Roitershtein

Random walks in random environments

October 17

Speaker - K. B. Athreya

Growth rates for pure birth Markov chains

October 10

Speaker - Sunder Sethuraman

On fractional Brownian motion limits in a simple exclusion random walk particle system

October 3

Speaker - Jiyeon Suh

Uniform learnability and VC dimension
Suh will recap the results and give some proofs.

September 26

Speaker - Jiyeon Suh

Uniform learnability and VC dimension

Valiant introduced the idea of learnability of a class of sets, which he called a concept class. Blumer, Ehrenfeucht, Haussler and Warmuth (1987) (henceforth referred to as BEHW) showed that a concept class is uniformly learnable( a property that will be defined in the talk) if and only if it is a VC class( a combinatorial property that will be defined in the talk). The aim of the talk is to explain the part of the BEHW paper that established the equivalence and to give a proof slightly different from that of BEHW.

September 12

Speaker - Alex Roitershtein

A random walk on Z with drift driven by its occupation time at zero

We consider a one-dimensional nearest neighbor random walk on the integer lattice with time-dependent drift towards the origin, given by an asymptotically vanishing function of the number of visits to zero. We obtain limit theorems for this random walk. In particular, we show the existence of three regimes according to the rate of decay of the drift. When the rate is sufficiently fast,
the random walk satisfies the invariance principle. When the rate is
sufficiently slow, the position of the random walk, properly scaled, converges to a symmetric exponential law.

This is a joint work with Iddo Ben-Ari (UC Irvine) and Mathieu Merle (UBC).