A Meinardus theorem with multiple singularities

Details A Meinardus theorem with multiple singularities A Meinardus theorem with multiple singularities

2011-02-28

arxiv.org/abs/1102.5608v2

Mathematics

Probability

26 pages. This version incorporates the following two changes implied by referee's remarks: (i) We made changes in the proof o

Scientific paper

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \cite{GSE}, we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size $n$, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.

Affiliated with

Also associated with

No associations

Rating

A Meinardus theorem with multiple singularities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Meinardus theorem with multiple singularities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Meinardus theorem with multiple singularities will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-424812