Robin Pemantle: Automatic Asymptotics for Multivariate Generating Functions

I will first discuss the general problem of determining asymptotics of the coefficients of a multivariate generating function. Next, I will discuss the special case where the function is the product of reciprocals of linear terms, arising for example in queuing applications (see [BM93]). It is possible in this case to give a precise algorithm for computing a finite collection of asymptotic formulae. I will present this, with indications of proofs. If time permits, I will discuss to what degree we know how to find such an algorithm in more general cases.


Andrea Bertozzi and James McKenna.
Multidimensional residues, generating functions, and their application to queueing networks.
SIAM Rev., 35(2):239-268, 1993.

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