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| Speaker |
Michael Marcus, City College |
|---|
| Title |
Two results on the continuity of stochastic convolutions. |
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|
| Speaker |
Ingrid-Mona Zamfirescu, Baruch College |
|---|
| Title |
Optimal Stopping under Model Uncertainty. |
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|
| Speaker |
Gennady Samorodnitsky, Cornell |
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| Title |
Ergodic theory and probabilistic properties of stationary stable processes |
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| Abstract |
While the probabilistic properties of stationary Gaussian
processes
are determined by the spectral measure via the covariance function,
different
tools are needed to understand the structure of stationary stable processes.
The appropriate tools here come from the ergodic theory of flows on measure
spaces. We present basic elements of the corresponding theory developed
by Jan Rosinski and show some recent results connecting the properties of
the flow to the properties of the stationary process. |
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|
| Speaker |
David Hobson, University of Bath and Princeton |
|---|
| Title |
Skorokhod Embeddings |
|---|
| Abstract |
Given a Markov process Xt and a distribution m, the Skorokhod
embedding problem is to find a stopping time t such that the stopped
process Xt has law m.
If X is Brownian motion and is centred then several explicit solutions
to the Skorokhod problem are known. In this talk we will review some of
these solutions, and give a "picture" within which many of the
constructions can be represented. If time permits we will move on to
consider how the story extends to diffusions (rather than just Brownian
motion) and to non-centered distributions.
|
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|
| Speaker |
Joseph E. Yukich , Lehigh University |
|---|
| Title |
Gaussian limits for random geometric structures |
|---|
| Abstract |
We describe general methods showing that
re-normalized weighted random point measures on Poisson and
binomial spatial point sets converge to a Gaussian limit with a
covariance functional depending on the underlying density of
points. The methods apply to point measures whose weights satisfy
a weak spatial dependence condition known as stabilization. The
general results are applied to deduce Gaussian central limit
theorems for measures and functionals arising in random sequential
packing and ballistic deposition models, random Euclidean graphs,
interacting particle systems in the continuum, and the process of
maximal points. In each case the large scale limit behavior of the
point measures is linked to the local behavior of the underlying
density of points. This is joint work with Y. Baryshnikov. |
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|
| Speaker |
Evarist Giné , University of Connecticut |
|---|
| Title |
The integrated squared error of kernel density estimators. |
|---|
| Abstract |
The a.s. size of the integrated squared error between a
kernel density estimator and its mean, and also between the estimator
and the true density are determined. The main tools are an adaptation
of Pinsky's proof of the LIL to Gaussian chaos and an exponential
bound of Giné, Latala and Zinn for U-statistics. This is joint
work with David M. Mason. |
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|
| Speaker |
Wenbo Li, Univ. of Delaware |
|---|
| Title |
Independent Constants and Some Gaussian Inequalities |
|---|
| Abstract |
Given d real valued random variables X1, ¼, Xd,
there are various ways to measure dependence structures among them, such
as correlations,
mixed moments, etc.
In this talk, we define and study a new measure that captures the amount
of dependence
when it is compared with the "best" independent ones.
To be more precise, we consider the
best (largest constant a and smallest constant b) possible
probability bounds
|
a |
d
Õ
i=1
|
P(Wi Î Bi) £ P( Çi=1d {Xi Î Bi} ) £ b |
d
Õ
i=1
|
P(Yi Î Bi) |
|
for some real valued random variables Wi, Yi,
and all Borel sets Bi, 1 £ i £ d.
The joint Gaussian case will be discussed in detail. |
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|
| Speaker |
Amir Dembo, City College, Stanford |
|---|
| Title |
Two problems in the asymptotics of large random matrices. |
|---|
| Abstract |
We show that the properly scaled spectral measures
of symmetric Hankel and Toeplitz matrices of size N by N generated by
i.i.d. random variables of zero mean and unit variance converge weakly
in N to universal, non-random, symmetric
distributions of unbounded support, whose moments are
given by the sum of volumes of solids related to Eulerian numbers.
The universal limiting spectral distribution for
large symmetric Markov matrices
generated by off-diagonal i.i.d. random variables
of zero mean and unit variance, is more explicit, having
a bounded smooth density given by the free convolution of the
semi-circle and normal densities.
Time permitting, I will also explain the formula for the
large deviations rate function
for the number of open path of length k in random graphs
on N >> 1 vertices with
each edge chosen independently with probability 0 < p < 1,
and more generally, for the same functionals applied
to any sequence of matrices with bounded i.i.d. entries.
Using the same rationale, we can guess the rate functions
for the number of simple cycles of length k > 2 in large
random graphs, the derivation of which is yet an open problem.
This talk is based on joint works with Wlodek Bryc, Francis Comets,
and Tiefeng Jiang.
|
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