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Distinguished Lecturer Series
Special Event
Sponsored by the Arthur and Rochelle Belfer
Institute of Mathematics and Computer Science
Sunday, 31 October 2010
Room 1, Ziskind Building
14:30 - 15:30
Constantine Dafermos
Brown University
Maximal Dissipation in Equations of Evolution
Abstract: The lecture will introduce examples of evolutionary equations with diverse provenances,
in which a certain energy functional is conserved along classical solutions, the initial value problem
generally admits a multitude of weak solutions, and argue that the solution along which the energy decays
at a maximum rate may have special status.
15:30 - 16:00: Coffee break
16:00 - 17:00
Srinivasa Varadhan
New York University
Large Deviations for Random Graphs
Abstract: In this joint work with Sourav Chatterjee, we consider a random
graph with n vertices, with probability
p for any given edge to be present. We consider the case when p is fixed and
n gets large. Asymptotically the
expected number of edges is ~1/2 n2 and the expected number of triangles is
~1/6 n3. We look at the large deviation
probabilities for these numbers as well as other subgraph counts. This
allows us to say, for example, what a graph
with more than the normal number of triangles will look like. The model
exhibits an interesting phase transition.
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