UCSD MATHEMATICS DEPARTMENT: PROBABILITY SEMINAR 2006-2007
The probability seminar meets at 10am on Thursdays in
AP&M 6402
unless specifically indicated otherwise.
Please address all inquiries to this year's seminar coordinator:
Professor Williams, williams at math dot ucsd dot edu
FALL 2006
Monday, October 2, 2006, noon, AP&M 6402
Related Seminar: Applications
Dr. M. Vidyasagar, Executive Vice President
Tata Consultancy Services Limited,
Hyderabad INDIA
Stochastic Modelling Methods for Gene Finding
For an abstract, click here.
Thursday, October 12, 2006.
Professor Youri Davydov,
University of Lille I, France
Ergodic properties of crystallization processes.
For an abstract, click here.
Thursday, October 19, 2006. Probability, Statistics and Biostatistics
Seminar: 10am.
Samuel Kou, Harvard University.
Stochastic modeling in single molecule biophysics.
For an abstract, click here.
Thursday, October 19, 2006. Special Probability Seminar: 2pm
Dimitri Gioev, University of Rochester.
Title: "Universality Questions in Random
Matrix Theory"
For an abstract, click here.
Thursday, October 26, 2006.
Michael Kinnally, graduate student, UCSD.
On "Qualitative behavior of stochastic delay equations
with bounded memory" following M. Scheutzow,
Stochastics, 12 (1984), 41-80.
Thursday, November 2, 2006
Priscilla Greenwood, Arizona State University
Autonomous stochastic resonance produces epidemic
oscillations of fluctuating size.
For an abstract,
click here.
Thursday, November 9, 2006
Jomy Alappattu, graduate student, UC Berkeley.
Fragmentation and coalescence of conditioned Galton-Watson forests.
For an abstract, click here.
Thursday, November 16, 2006
Michael Cranston, UC Irvine
Large deviations for parabolic Anderson and other random media models.
For an abstract, click here.
Friday, November 17, 2006
San Diego Chapter of the American Statistical Association,
One day conference
Thursday, November 30, 2006
S. Molchanov, UNC Charlotte, visiting UCI.
On a class of differential-functional equations.
For an abstract, click here.
Wednesday, December 6, 2006, 1pm, PLEASE NOTE SPECIAL TIME
Colloquium
Nathanael Berestycki, University of British Columbia
Random walks, geometry and comparative genomics.
For an abstract, click here.
Thursday, December 7, 2006
Nathanael Berestycki, University of British Columbia.
Hydrodynamic limits of spatially structured coalescents.
For an abstract, click here.
WINTER 2007
Please note that many talks for Winter are on unusual days and
at unusual times.
Thursday, January 18, 2007, 10am.
Ery Arias-Castro, UCSD.
Searching for a Trail of Evidence in a Maze.
For an abstract, click here.
Tuesday, January 23, 2007, 4pm. (Probability) Colloquium.
Note special day and time.
Julien Dubedat, Courant Institute.
"Schramm-Loewner Evolutions on Riemann surfaces"
Weeklong conference, January 29-February
2, 2007.
Information
Theory and Its Applications, Workshop, UCSD,
If you are planning to attend, please register. The cost is
minimal to cover catering. Registration can be done for just
the days that you plan to attend.
Monday, February 5, 2007, noon.
Note special day and time.
Special Probability and Applications Seminar.
Professor Frank Kelly, University of Cambridge
Flow level models of Internet congestion control
Abstract:
Variability in the number of simultaneous flows present
can have a substantial impact on the perceived performance
of packet networks such as the Internet. While the packet level
behaviour of a given set of flows is by now well understood,
less is known about the stochastic behaviour of the number of
flows in progress on different routes through the network.
In this talk we describe recent work on Brownian models of
networks in heavy traffic.
Joint work with Ruth Williams.
Sunday, February 11, 2007.
Southern California Probability Symposium/Conference in Honor of Ted Harris, USC.
Thursday, February 22, 2007, 10 am.
Keh-Shin Lii, UC Riverside, visiting UCSD.
Modeling Marked Point Processes.
Abstract:
New probability models are proposed for the analysis of marked point
processes. These models deal with the type of data that arrive
or are observed in possibly unequal time intervals such as
financial transactions, earthquakes among others. The models
treat both the time between event arrivals and the observed marks
as stochastic processes. We adopt a class of bivariate
distributions to form the bivariate mixture transition
distribution(BMTD). In these models the
conditional bivariate distribution of the next
observation given the past is a mixture of conditional
distributions given each one of the last p observations or a
selection of past p events. The identifiability of the model is
investigated, and EM algorithm is developed to obtain estimates
of the model parameters. Simulation and real data examples are
used to demonstrate the utility of these models.
Thursday, March 1, 2007, 10 am.
Rafael De Santiago, Graduate student, UC Irvine.
"Interest Rate Markets with Stochastic Volatility". For an
abstract, click here.
Thursday, March 8, 2007, 10 a.m.
Sebastien Roch, graduate student, UC Berkeley.
Markov Models on Trees: Reconstruction and Applications
Abstract:
Markov models on trees arise naturally in many fields, notably in molecular
biology - as models of evolution; in statistical physics - as models of
spin systems; and in networking - as models of broadcasting. In this talk,
I will discuss various inference problems motivated especially by
applications in statistical phylogenetics, i.e. the reconstruction of
evolutionary histories of organisms from their molecular sequences. In
particular, I will consider the "root reconstruction" problem: how
accurately can one guess the value at the root of the tree, given the state
at the leaves? I will focus on recent work establishing new conditions for
the impossibility of such reconstruction. I will also discuss the related
"phylogenetic reconstruction" problem: given enough samples at the leaves,
can one reconstruct the tree that generated this data and, if so, how
efficiently? I will present a recent result on a sharp transition in the
number of samples required to recover the tree topology, using a connection
to the root reconstruction problem above. Time permitting, I will describe
briefly connections to computational learning theory and network tomography
as well. This is joint work with S. Bhamidi, C. Borgs, J. Chayes, C.
Daskalakis, E. Mossel, and R. Rajagopal.
Thursday, March 15, 10 am.
Denis Bell, University of North Florida.
"Quasi-invariant measures on path space".
Abstract: "Let $N$ denote a manifold equipped with a finite Borel measure
$\gamma$. A vector field $Z$ on $N$ is said to be admissible with respect
to $\gamma$
if $Z$ admits an integration by parts formula. The measure $\gamma$ is
said to be quasi-invariant under $Z$
if the class of null sets of $\gamma$ is preserved by the flow generated
by $Z$. In this talk we study the law $\gamma$ of an elliptic
diffusion process with values in a closed compact manifold. We construct a
class of admissible vector fields for $\gamma$, show that $\gamma$
is quasi-invariant under these vector fields, and give a formula for the
associated family of Radon-Nikodym derivatives $d\gamma_s\over d\gamma$.
Conference, March 15-17, 2007.
Seminar on Stochastic Processes, Fields Institute, Toronto ON.
SPRING 2007
Thursday, April 12, 2007, 10am.
Jacek Leskow (Nowy Sacz, Poland, visiting UCSD)
"Relative measurability and time series analysis. A non-stochastic
perspective."
Abstract:
The concept of relative measure was fairly popular among Polish
mathematicians of 1930 in Lvov. Steinhaus and Urbanik were working
on introducing a relative measure and relative measurability into
the area of random variables.
Recent work on signal processing and time series has led to
re-discovery of the 'old-school' theorems and application to
data generated by signals or time-series. Some fundamental work
was done by Garnder and continuation of this work was done
by Leskow and Napolitano.
A short informal introduction to a nonstochastic approach
to time series inference via relative measurability will
be presented. Applications to signal forecasting will be
presented.
Thursday, April 19, 2007, 10am.
Professor Ron Getoor, UCSD.
Walsh's interior reduite
Abstract: This will be an expository talk. I'll begin by
introducing the concepts of reduite (reduced function) and balayage
(swept measure) in classical potential theory and their
interpretations in terms of Brownian motion. I'll then discuss the
extension of these ideas to Markov processes as in Hunt's fundamental
memoir. After introducing h-transforms I'll be able to define the
interior reduite and discuss some of its properties following Walsh.
If time permits I'll give some indications of recent work in this
area by Fitzsimmons and myself.
Thursday, May 3, 2007, 10am.
Vladimir Rotar, San Diego State University
On asymptotic proximity of probability distributions
and the non-classical invariance principle.
Abstract:
Usually, a limit theorem of Probability Theory is a theorem that concerns convergence of
a sequence of distributions P_n to a distribution P. However, there is a number of works
where the traditional setup is modified, and the object of study is two sequences of
distributions, P_n and Q_n, and the goal consists in establishing conditions implying
the convergence
P_n - Q_n ->0
(1)
In particular problems,P_n and Q_n are, as a rule, the distributions of the
r.v.'s f(X_1,...,X_n) and f(Y_1,...,Y_n) , where f(.) is a function, and X_1,X_2,...
and Y_1,Y_2,... are two sequences of r.v.'s. The aim here is rather to show that
different random arguments X_1,...,X_n may generate close distributions of
f(X_1,...,X_n) , than to prove that the distribution of f(X_1,...,X_n) is close to
some fixed distribution (which, above else, may be not true).
Clearly, such a framework is more general than the traditional one. First, as
was mentioned, the distributions P_n and Q_n, themselves do not have to converge.
Secondly, the sequences P_n and Q_n are not assumed to be tight, and the convergence in
(1) covers situations when a part of the probability mass or the whole distributions
"move away to infinity'", while the distributions P_n and Q_n, are approaching each
other.
We consider a theory on this point, including the very definition of convergence (1),
and a particular example of the invariance principle in the general non-classical setup.
Thursday, May 17, 2007, 10am.
Professor Guillaume Bonnet, UC Santa Barbara
"Non-linear SPDEs for Highway Traffic Flows:
Theory, and Calibration to Traffic Data"
Abstract:
Highway traffic flows are generally modeled by partial differential equations
(PDEs). These models are used by traffic engineers for
road design, planning or management. However, they
often fail to capture important features of
empirical traffic flow studies, particularly at small
scales. In this talk, I will propose a fairly simple stochastic model for
highway traffic flows in the form of a nonlinear stochastic partial differential
equation (SPDE) with random
coefficients driven by a Poisson random measure. I will discuss the
well posedness of the proposed equation as well as the
corresponding inverse problem that I will illustrate by its
calibration to high resolution traffic data from highway
101 in Los Angeles. I will also present a more sophisticated spde
in the form of a system of coupled hyperbolic-parabolic equations.
Monday, June 11, 2007, 11 am, AP&M 6402. (Please note unusual
time and day)
Professor Mor Harchol-Balter (Computer Science Department, Carnegie Mellon University).
"Analysis of Join-the-Shortest-Queue Routing
in Web Server Farms"
ABSTRACT:
We present the first analysis of the Join-the-Shortest-Queue (JSQ)
routing policy for Web server farms. Web server farms involve a
collection of Processor-Sharing (PS) servers, whereas prior analyses
of JSQ have always assumed First-Come-First-Serve (FCFS) servers.
This work introduces a new technique: Single-Queue-Approximation
(SQA), and uses the technique to prove some interesting insensitivity
properties for Web server farms.
Joint with: Varun Gupta, Karl Sigman, and Ward Whitt.
Wednesday, August 1, 2007, 11am. AP&M 6402. (Please note
unusual day and time.)
James Norris, Cambridge University.
Planar aggregation and the coalescing Brownian flow.