[Ml-stat-talks] APC 550: Probability in High Dimension (Fall 2016)

Ramon van Handel rvan at Princeton.EDU
Sat Sep 10 21:08:27 EDT 2016


Dear all,

I will be teaching a topic course this semester (starting on Wednesday) 
on Probability in High Dimension that is intended to be useful for 
graduate students in probability, statistics, computer science, and 
applied math. The syllabus is included at the end of this email.

This is the second time such a course is being offered. Lecture notes from the 
previous incarnation can be downloaded here:

http://www.princeton.edu/~rvan/ORF570.pdf

The intention this year is to cover some part of this material, and then to 
move on to a number of new topics that have not been covered previously. In 
particular, I aim to include this year topics such as hypercontractivity, 
threshold phenomena, and universality.

All the best, -- Ramon

---------

APC/ORF 550: Probability in High Dimension (Fall 2016)

The aim of this course is to provide an introduction to nonasymptotic methods 
for the study of random structures in high dimension that arise in probability, 
statistics, computer science, and mathematics. The emphasis is on the 
development of a common set of tools that has proved to be useful in a wide 
range of applications in different areas. Topics may include, depending on time 
and the interests of the audience: concentration of measure; functional, 
transportation cost, martingale inequalities; isoperimetry; Markov semigroups, 
mixing times, random fields; hypercontractivity; thresholds and influences; 
Stein's method; suprema of random processes; Gaussian and Rademacher 
inequalities; generic chaining; entropy and combinatorial dimensions; selected 
applications.

Prerequisites. A working knowledge of probability theory (e.g., ORF 526).

Course time: Mondays and Wednesdays, 9:30-10:50 AM, Fine Hall 601.

Course materials: Lecture notes.

Grading. Number of homework assignments to be determined based on enrollment 
and teaching staff. A final project will due at the end of the semester; the 
aim is to give each student the opportunity to apply the material to her/his 
own area of interest. There are no exams. Additional points may be available 
for serving as a scribe during some lectures.



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