Physics – Mathematical Physics
Scientific paper
2011-10-19
Physics
Mathematical Physics
Replaces v2 which contains typographical errors arising from a previous unpublished draft
Scientific paper
An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix $\beta$-ensembles. The conditioning is that there are $n$ eigenvalues in the gap, with $n \ll |t|$, $t$ denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consistent with known asymptotic expansions in the case $n=0$. With this modification made for general $n$, the derived expansions - which are for the logarithm of the gap probabilities - are conjectured to be correct up to and including terms O$(\log|t|)$. They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating $\beta$ to $4/\beta$.
Forrester Peter J.
Witte Nicholas S.
No associations
LandOfFree
Asymptotic forms for hard and soft edge general $β$ conditional gap probabilities 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 Asymptotic forms for hard and soft edge general $β$ conditional gap probabilities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic forms for hard and soft edge general $β$ conditional gap probabilities will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-597413