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MATH 705, Seminar in Probability (39948R), Spring 2017.

Class meetings: M 10am-12pm, in KAP 427.

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Information on this and linked pages changes frequently.

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** Organizer: **
Sergey Lototsky.

** Office:** KAP 248D.

** Phone:** (213) 740-2389.

Office Hours: MWF 2-3pm.

Walk-ins and appointments at other time are welcome.

** The objective this semester: ** To discuss current research projects and future plans of participating students.

** Participating students: **
Mark Duggan,
Hyun-Jung Kim,
Alperen Ozdemir,
Jian Wang,
Fanhui Xu.

** What we did **

Monday, January 9: Introduction and general discussion. A possible question to
think about and
discuss throughout the semester: what can we say about the eigenvalues
of a square matrix with iid Levy processes as entries? While we might not be
able to say much, we should learn, and try to connect,
some ideas about Levy processes,
random matrices, Tracy-Widom distributions, Malliavin calculus, and maybe
large deviations and optimal control.

Monday, January 16: MLK Day.

Monday, January 23: A (long) presentation by Fanhui on Levy processes, followed by a
(short) presentation by Alperen on (random) Wigner matrices.

Monday, January 30: A white-board presentation by Alperen on period-two Markov chains on the symmetric
group.

Monday, February 6: A presentation by Hyun-Jung on the parabolic Anderson model.

Monday, February 13: A computer presentation by Alperen on period-two Markov chains on the symmetric
group (practice for the oral exam).

Monday, February 20: Presidents Day.

Monday, February 27: A presentation by Hyun-Jung on Bernoulli traps.

Monday, March 6: A presentation by Jian on time series, in particular, the unit
root processes.

Monday, March 13: Spring Break.

Monday, March 20: A practice presentation by Fanhui for the oral exam

Monday, March 27: Practice presentations by Hyun-Jung and Fnahui for an
upcoming conference.

Monday, April 3: A presentation by Mark on KL divergence.

Monday, April 10: A discussion of career plans of participating students.

Monday, April 17: A discussion of random matrices with Levy processes as
entries.

Monday, April 24: A presentation by Jian on large deviations/optimal control
approach to the study of coupled diffusions with a small parameter.