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Mark Kac
Pages 214-235

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From page 215... ... 61. In this connection Kac liked to quote Hugo Steinhaus, who, when asked if he had crossed the border repliecl, "No, but the border crossed me." In the early days of the century Krzemieniec was a predominantly Jewish town surrounded by a Polish society generally hostile to Jews. Read the entire page →
From page 216... ... teacher who became his true friend and introduced him to the then undigested subject of probability. Kac would devote most of his scientific life to this field and to its cousin, statistical mechanics, beginning with a series of papers prepared jointly with Steinhaus on statistical indepenclence ~1936, I-4; and 1937, I-21. Read the entire page →
From page 217... ... There DetIev Bronk, with his inimitable enthusiasm, was trying to build up a small, top-flight school. While this ideal was not fully realized either then or afterwards, it afforded Kac the opportunity to immerse himself in the statistical mechanics of phase transitions in the company of Tect Berlin and UhIenbeck, among others. Read the entire page →
From page 218... ... , but as Poincare complained, "Tout le monde y croft (la loi des erreurs) parce que les mathe'maticiens s'imaganent que c'est un fait d'observation et les observateurs que c'est un the'oreme de mathe'matiques." The missing ingredient, suppliecl by Steinhaus, was an unambiguous concept of indepenclence. Read the entire page →
From page 219... ... . Brownian Motion and Integration in Function Space The Brownian motion typified by the incessant movement of dust motes in a beam of sunlight was first discussed from a physical standpoint by M Read the entire page →
From page 220... ... Now the statistical law of the Brownian motion is normal: if Aft) is the displacement of the Brownian traveler in some fixed direction, then PLa c x~t) Read the entire page →
From page 221... ... It can be used very electively, as Kac illustrated by a beautiful derivation of the WKB approximation of classical quantum mechanics (1946,31. ~ will describe one more application of Brownian motion contained in Kac's Chauvenet Prize paper, Can One Hear the Shape of a Drum? Read the entire page →
From page 222... ... and a typically elegant, Kac-type "caricature" of the Boltzmann equation itself. ~ pass on to the eminently successful papers on phase transitions. Read the entire page →
From page 223... ... He mistrusted as insufficiently digestecl anything that required fancy technical machinery to the extent that he would sometimes insist on clumsy but elementary methods. ~ user! Read the entire page →
From page 224... ... 224 BIOGRAPHICAL MEMOIRS his wit and kindliness. Such stories are innumerable, but ~ reproduce here a favorite Kac himself recorded in his autobiography: "The candidate [at an oral examination] Read the entire page →
From page 225... ... D Birkhoff Prize, American Mathematical Society Kramers Professor, Utrecht Fermi Lecturer, Scuola Normale, Pisa 968 968 969 969 969 971 976 978 980 980 225 Read the entire page →
From page 226... ... Math., 6:46-58. Quelques remarques sur les fonctions independantes. Read the entire page →
From page 227... ... A., 3:151-53. 1943 On the average number of real roots of a random algebraic equation. Read the entire page →
From page 228... ... I., 12: 189-206. A remark on independence of linear and quadratic forms involving independent Gaussian variables. Read the entire page →
From page 229... ... The distribution of the maximum of partial sums of independent random variables. Canad. Read the entire page →
From page 230... ... Toeplitz matrices, translation kernels and a related problem in probability theory. Read the entire page →
From page 231... ... 165-69. 1963 Probability theory as a mathematical discipline and as a tool in engineering and science. Read the entire page →
From page 232... ... Mathematical mechanisms of phase transitions. In: 1966 Brandeis Summer Inst. Read the entire page →
From page 233... ... 197 The role of models in understanding phase transitions. In: Critical Phenomena in Alloys, Magnets and Superconductors, ed. Read the entire page →
From page 234... ... Phys., 14:594-603. Lectures on mathematical aspects of phase transitions: NATO Summer School in Math. Read the entire page →
From page 235... ... On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices. Read the entire page →

From page 215...

... 61. In this connection Kac liked to quote Hugo Steinhaus, who, when asked if he had crossed the border repliecl, "No, but the border crossed me." In the early days of the century Krzemieniec was a predominantly Jewish town surrounded by a Polish society generally hostile to Jews.

Mark Kac Pages 214-235

Mark Kac
Pages 214-235