General Prerequisites: Part A Probability and Part A Integration are required.
Course Overview: High-dimensional probability and high-dimensional statistics have
emerged in recent years as ever more important topics due to the need to analyse
vast amounts of complex data. The ideas and methods developed for dealing
with probability distributions on spaces of high-dimension
(such as distributions of randomly sampled data with multiple attributes)
have been used not only in pure mathematics but also in applications
from stochastic simulation to statistics, data science to statistical mechanics.
This course will focus on the development of basic ideas and techniques
such as elementary dimension-free tail estimates, concentration
bounds, the metric entropy method, the Poincare and logarithmic
Sobolev inequalities, large deviation principles for rare events etc.
Learning Outcomes: The students will learn the fundamental ideas and modern tools for
handling distributions on high-dimensional spaces, and understand
some special features of probability distributions on such spaces, for example
the concentration of probability laws on small regions of low dimensional
subspaces.
