Mathematics – Probability
Scientific paper
2008-11-12
Annals of Probability 2010, Vol. 38, No. 2, 714-769
Mathematics
Probability
Published in at http://dx.doi.org/10.1214/09-AOP493 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Scientific paper
10.1214/09-AOP493
Consider $n+m$ nonintersecting Brownian bridges, with $n$ of them leaving from 0 at time $t=-1$ and returning to 0 at time $t=1$, while the $m$ remaining ones (wanderers) go from $m$ points $a_i$ to $m$ points $b_i$. First, we keep $m$ fixed and we scale $a_i,b_i$ appropriately with $n$. In the large-$n$ limit, we obtain a new Airy process with wanderers, in the neighborhood of $\sqrt{2n}$, the approximate location of the rightmost particle in the absence of wanderers. This new process is governed by an Airy-type kernel, with a rational perturbation. Letting the number $m$ of wanderers tend to infinity as well, leads to two Pearcey processes about two cusps, a closing and an opening cusp, the location of the tips being related by an elliptic curve. Upon tuning the starting and target points, one can let the two tips of the cusps grow very close; this leads to a new process, which might be governed by a kernel, represented as a double integral involving the exponential of a quintic polynomial in the integration variables.
Adler Mark
Ferrari Patrik L.
Moerbeke Pierre van
No associations
LandOfFree
Airy processes with wanderers and new universality classes 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 Airy processes with wanderers and new universality classes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Airy processes with wanderers and new universality classes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-100889