Conditional Haar measures on classical compact groups

Details Conditional Haar measures on classical compact groups Conditional Haar measures on classical compact groups

2008-03-26

arxiv.org/abs/0803.3753v2

Annals of Probability 2009, Vol. 37, No. 4, 1566-1586

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AOP443 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/08-AOP443

We give a probabilistic proof of the Weyl integration formula on U(n), the unitary group with dimension $n$. This relies on a suitable definition of Haar measures conditioned to the existence of a stable subspace with any given dimension $p$. The developed method leads to the following result: for this conditional measure, writing $Z_U^{(p)}$ for the first nonzero derivative of the characteristic polynomial at 1, \[\frac{Z_U^{(p)}}{p!}\stackrel{\mathrm{law}}{=}\prod_{\ell =1}^{n-p}(1-X_{\ell}),\] the $X_{\ell}$'s being explicit independent random variables. This implies a central limit theorem for $\log Z_U^{(p)}$ and asymptotics for the density of $Z_U^{(p)}$ near 0. Similar limit theorems are given for the orthogonal and symplectic groups, relying on results of Killip and Nenciu.

Affiliated with

Also associated with

No associations

Rating

Conditional Haar measures on classical compact groups 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 Conditional Haar measures on classical compact groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conditional Haar measures on classical compact groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-50078