*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. - 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.

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

Posted at February 28, 2006 23:59 | permanent link