Seminars and Colloquia by Series

Topics in Sequence Analysis

Series
Dissertation Defense
Time
Monday, November 5, 2012 - 12:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 005
Speaker
Jinyong MaSchool of Mathematics, Georgia Tech
This work studies two topics in sequence analysis. In the first part, we investigate the large deviations of the shape of the random RSK Young diagrams, associated with a random word of size n whose letters are independently drawn from an alphabet of size m=m(n). When the letters are drawn uniformly and when both n and m converge together to infinity, m not growing too fast with respect to n, the large deviations of the shape of the Young diagrams are shown to be the same as that of the spectrum of the traceless GUE. Since the length of the top row of the Young diagrams is the length of the longest (weakly) increasing subsequence of the random word, the corresponding large deviations follow. When the letters are drawn with non-uniform probability, a control of both highest probabilities will ensure that the length of the top row of the diagrams satisfies a large deviation principle. In either case, speeds and rate functions are identified. To complete this first part, non-asymptotic concentration bounds for the length of the top row of the diagrams are obtained. In the second part, we investigate the order of the r-th, 1\le r < +\infty, central moment of the length of the longest common subsequence of two independent random words of size n whose letters are identically distributed and independently drawn from a finite alphabet. When all but one of the letters are drawn with small probabilities, which depend on the size of the alphabet, the r-th central moment is shown to be of order n^{r/2}. In particular, when r=2, the order of the variance is linear.

On the Almost Axisymmetric Flows with Forcing Terms

Series
Dissertation Defense
Time
Tuesday, June 19, 2012 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Marc SedjroSchool of Mathematics, Georgia Tech
This work is concerned with the Almost Axisymmetric Flows with Forcing Terms which are derived from the inviscid Boussinesq equations. It is our hope that these flows will be useful in Meteorology to describe tropical cyclones. We show that these flows give rise to a collection of Monge-Ampere equations for which we prove an existence and uniqueness result. What makes these equations unusual is the boundary conditions they are expected to satisfy and the fact that the boundary is part of the unknown. Our study allows us to make inferences in a toy model of the Almost Axisymmetric Flows with Forcing Terms.

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