On the size of the Durfee square of a random integer partition

We prove a local limit theorem for the length of the side of the Durfee square in a random partition of a positive integer n as n --> infinity. We rely our asymptotic analysis on the power series expansion of x(m2) Pi(j=1)(m)(1-x(j))(-2) whose coefficient of x(n) equals the number of partitions of n in which the Durfee square is m(2). (C) 2002 Elsevier Science B.V. All rights reserved.