You are here

Chance and Choice: Memorabilia

Kai Lai Chung
World Scientific
Publication Date: 
Number of Pages: 
[Reviewed by
Stacy Langton
, on

Kai Lai Chung is an eminent probabilist, now emeritus professor at Stanford. Born in Shanghai, China, (the meaning of the caption to photo number 13 of the book under review, which describes Hangzhou as "the author's native town", is that it is the town of his ancestors) in 1917, he graduated in 1940 from Tsinghua University at Kunming, where he studied with Pao Lu Hsu (Xu Bao-lu). He came to the United States in 1945, and obtained his Ph.D. at Princeton in 1947, under Cramér.

Chung has published many books, including undergraduate- and graduate-level textbooks in probability. I have had the pleasure of teaching an undergraduate course in probability from his book Elementary Probability Theory with Stochastic Processes, now in a fourth edition with new co-author Farid AitSahlia (Springer, 2003).

Chance and Choice: Memorabilia is a collection of Chung's papers, some of them research papers, some expository, some reviews. Most are connected in one way or another with the theory of Markov chains, though there are excursions into combinatorics. Even Jacobian theta-functions make an appearance. Most of the papers are in English, three are in French and one is in Italian. The contents and tragic circumstances of the one paper in Chinese are explained in the preceding paper in English. (The reader should be warned that the printer has interchanged page 2 and page 3. I can't resist pointing out here that the fundamental summation (8) that Chung uses in this first paper [p. 2] is an instance of the formula

which ought to be as familiar as the corresponding integration formula, but somehow is not. Here kn is the "falling power":

kn = k(k - 1)...(k - n + 1).

As Prof. Chung frequently remarks, "Notation can be incredibly important!")

There are occasional minor infelicities of language, hard to avoid entirely for a writer whose native tongue is not English. (For example, on p. 269 he refers to a "splightly author" — presumably intending "sprightly".) Despite these, Chung's writing is literate, elegant, wise, humane. He takes the reader into his confidence, explaining ideas, motivation, and circumstances. There are frequent aperçus. For example (p. 141), the article "Markov chain must have a beginning" begins, "The proposition quoted in the title above is a folklore. It can be argued as follows. If a Markov chain has run an infinitely long time, then every 'state' will have become a 'steady state', and nothing will happen any more. This is physicists' talk, which sounds apt for the occasion."

There are old photos of Chung with Cramér, Feller, Erdös, and others.

You probably won't want to buy this book unless you are a specialist in probability, or intend to become one. Nevertheless, it is well worth browsing through in the library. Look at the last article, "Mathematics and Applications". Has Chung overstated the case for the non-usefulness of mathematics? See what you think.

Stacy G. Langton ( is Professor of Mathematics and Computer Science at the University of San Diego. He is particularly interested in the works of Leonhard Euler, a few of which he has translated into English.

* On Mutually Favorable Events
* On Fluctuations in Coin-Tossing
* On a Stochastic Approximation Method
* On the Martin Boundary for Markov Chains
* A Cluster of Great Formulas
* Probabilistic Methods in Markov Chains
* Markov Processes with Infinities
* Probability Methods in Potential Theory
* P¢lya's Work in Probability
* Probability and Doob
* In Memory of L‚vy and Fr‚chet
* and other papers