Index of /~pollard/Books/Pttm

	Name	Last modified	Size	Description
	Parent Directory		-
	BinFriends3jan21.pdf	2024-09-30 14:08	437K
	Calculus30may25.pdf	2025-05-30 14:32	558K
	Chaining5jul25.pdf	2025-07-05 14:47	799K
	MGF9jul25.pdf	2025-07-09 19:50	520K
	MVN6feb24.pdf	2025-03-05 18:55	485K
	Majorizing19apr24.pdf	2024-04-19 11:50	456K
	Orlicz6jul25.pdf	2025-07-06 21:12	409K
	Partitions15mar24.pdf	2024-03-15 15:12	1.3M
	Subexp11sept2021.pdf	2021-09-11 00:15	483K
	Subgaussian23oct23.pdf	2024-03-02 14:33	350K
	Symmetrization19feb2..>	2025-02-19 15:59	693K
	TOC2025-03-17.pdf	2025-03-17 17:48	217K
	VCsets22mar25.pdf	2025-03-22 13:26	1.1M
	Woes30jun23.pdf	2023-06-30 15:00	304K
	_TOC19feb25.pdf	2025-02-19 16:49	217K

Pollard Lectures 2023

• Time: Fridays 1:00--2:15, starting 6 October 2023
• Place: Kline Tower Room 1327

For many years I have have been working on a manuscript, tentatively called Probability tools, tricks, and miracles, that collects together a range of ideas that have been useful to me while working on statistical problems. My aim has been to simplify and, where possible, improve and extend a collection of tools that are scattered throughout the literature. I have also tried to understand why particular methods work and what limitations they have.

At the moment the manuscript runs to a little over 400 pages. (See current table of contents.) Chapters 2 through 12 are in what I hope is final form. The other chapters still need a lot of editing. Unfortunately, I have not yet had a chance to test the ideas on a live audience. Hence this set of 5 lectures.

I'll be assuming a little bit of 600-level probability. (For example, I want to explain convexity of the log MGF by means of an exponential tilting.) I also want to use P instead of E, of course. My aim is to convey the main ideas, leaving it up to the enthusiastic to read the details in my manuscript. I also plan to hang around after the lectures in case anyone wants to dig more deeply into the material.

My current plan:

• (2 lectures?) Tail bounds from MGF's (moment generating functions). Standard cases (eg, N(0,1) and Poisson) and cases where we have good upper bounds for the MGF (eg. Hoeffding and Bennett). Extensions to martingales (eg. bounded differences). See attached chapter, MGF.pdf.
• (1 lecture?) Path methods for the multivariate normal. Concentration of lipschitz functions under the N(0, I_n). Concentration of the maximum for a general multivariate normal. Maybe, mention comparison methods (eg. Fernique). See attached chapter, Gaussian.pdf.
• (2 lectures?) Chaining constructions. Why does it work? Classical packing/covering number constructions. Maybe mention some of the fancier methods derived from the 'majorizing measure' idea.

More lectures would be needed if anyone wanted to hear about VC classes and their modern extensions, or if anyone wanted to get into the details related to majorizing measures and Talagrand's "generic chaining".