Asymptotics of multinomial sums and identities between multi-integrals

We calculate the asymptotics of combinatorial sums f () (n)3 where = (l, . . ., h) with i = j. Here h is fixed and the i's are natural numbers. This implies the asymptotics of the corresponding Sn-character degrees f ()d3. For certain sequences of Sn characters which involve Young's rule, the latter asymptotics were obtained earlier [1] by a different method. Equating the two asymptotics, we obtain equations between multi-integrals which involve Gaussian measures. Special cases here give certain extensions of the Mehta integral [5], [6].

Asymptotics of multinomial sums and identities between multi-integrals Academic Article