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Series: Dissertation Defense

Series: Dissertation Defense

Series: Dissertation Defense

Series: Dissertation Defense

Series: Dissertation Defense

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.

Series: Dissertation Defense

Please see http://www.aco.gatech.edu/dissert/asadi.html for further details.

Series: Dissertation Defense

Details can be found at http://www.aco.gatech.edu/dissert/postle.html.

Series: Dissertation Defense

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.

Series: Dissertation Defense

Series: Dissertation Defense