Three-Toed Sloth

Books to Read While the Algae Grow in Your Fur, February 2006

Attention conservation notice: I have no taste.

Ian Kershaw, Hitler, 1889--1936: Hubris

There is something perversely mesmerizing about a bohemian crank becoming master of Europe, with nothing more to recommend him than his ability to express pathological hatred... But Kershaw is very good at showing at once how Hitler fit the circumstances he was in, without being in any way inevitable: he benefitted enormously, crucially, from choices other people made, and they didn't have to make them — unless being a reactionary idiot constitutes a condition of diminished responsibility.

--- Sequel.

Robert O. Paxton, The Anatomy of Fascism

Nice comparative history of fascist movements, with sharp observations, especially about how one of their distinguishing characteristics was a desire to maintain wide-scaled political mobilization after they'd attained power, and the crucial role of non-fascist conservatives and vested interested in promoting them (which is not to say that the fascists were just instruments of the bourgeoise). Also, some shrewd-sounding guesses about how future fascist movements might look in, e.g., the US. But not enough comparisons with non-fascist movements...

Appearances to the contrary notwithstanding, I did not actually spend all my time in February reading about fascists. In fact, most of my reading was in these books, though I didn't go cover to cover:

J. L. Doob, Stochastic Processes

Since 1953, pretty much every new textbook on stochastic processes in general (including a certain set of lecture notes) has been a lower and distorted version of this. Re-reading it reminds me why it is very hard to break out of this pattern... (No purchase link, because the price Wiley charges for their flimsy paperback edition is unconscionable. You're better off looking for a used copy of the hardback, and the world would be better off if Wiley would let a decent reprint publisher take it up.)

Michel Loève, Probability Theory

Another one of the classics, which I was revisiting for the very limited purpose of stealing what he had to say about second-order processes (this being the Loeve of the Karhunen-Loève theorem). And you have to love a math book dedicated to the authors' fellow concentration-camp internees (remembering, in the words of the poet, "Human reason is beautiful and invincible...").

I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes

This is an "Introduction" for people who are already familiar with measure-theoretic probability (though there is a one-chapter summary, intended as a refresher). It is at once quite thorough, and assumes a high level of mathematical maturity and comfort with abstractions, and very practical, and assumes the reader doesn't mind pages of calculations. (This strikes me as very Soviet.) A good value for the money.

Update, 2011: By "very Soviet" I meant very characteristic of mathematical writing from the (then) USSR, not any reflection on the larger culture. (How would I know about that?)

Stewart N. Ethier and Thomas G. Kurtz, Markov Processes: Characterization and Convergence

Do not start reading from the beginning, which is several chapters of fairly turbid linear-operator theory, followed by a chapter of utterly opaque weak-convergence-under-the-Skorokhod-topology. Instead, start with the material on actual Markov processes, and then work backwards through the foundational chapters as needed. (The flow-chart at the end of the book, indicating which results depend on which previous ones, is very helpful for this.) There is a wealth of fascinating material here, of profound importance for statistics and for physics, since both rely crucially on extracting nearly-deterministic behavior from large-scale Markov processes, which is a key theme of these results.

Olav Kallenberg, Foundations of Modern Probability

This is intended as something in the same mold as Loeve's book, developing probability from basic measure theory up through advanced topics in stochastic processes. Almost everything I want to teach is in here, and, while the proofs are often quite compressed, it is character-building for my students (and me!) to fill things in. Pretty much every topic of contemporary interest to probability theorists gets covered; but coverage is very much dictated mathematical, rather than by statistical or physical, interest. Kallenberg is fond of revisiting previously-introduced themes, which is pedagogically sound — and would work better, in a reference book, if the index were more detailed. Still, this is the best one-volume synthesis of modern probability I have encountered, and has become my default reference. If you could only have one book on advanced probability, I'd recommend this one.

L. C. G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales (in two volumes: Foundations and Itô Calculus)

I have to say that this is very much a mathematician's view of stochastic processes, and that I frankly don't see the point, for applications, of a lot of what gets them excited --- though, following them, I can get excited about it as pure math! And they're really very good at logically and comprehensively developing a mathematical theory.

It was striking how ugly Ethier and Kurtz's book is, on on the page, and Gikhman and Skorokhod and (it must be said) Doob aren't much better. Loeve, and Rogers and Williams, are better designed, and Kallenberg is actually, to my eye, fairly attractive.

Books to Read While the Algae Grow in Your Fur; Enigmas of Chance; Writing for Antiquity; The Running-Dogs of Reaction