Tcjk Fu I

An Almanack for the Year of Our Lord ...

Combinatorics and Random Matrix Theory

Over the last fifteen years a variety of problems in combinatorics have been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a “stochastic special function theory” for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.

Approaching Ottoman History

Suraiya Faroqhi's scholarly contribution to the field of Ottoman history has been prodigious. Her latest book represents a summation of that scholarship, an introduction to the state-of-the-art in Ottoman history. In a compelling exploration of the ways that primary and secondary sources can be used to interpret history, the author reaches out to students and researchers in the field and in related disciplines to familiarise them with these documents. By considering both archival and narrative sources, she explains why they were prepared, encouraging her readers to adopt a critical approach to their findings, and disabusing them of the notion that everything recorded in official documents is necessarily true! While the book is essentially a guide to a complex discipline for those about to embark upon their research, the experienced Ottomanist will find much that is original and provocative in its sophisticated interpretation of the field.