Continuum statistics of the Airy2 process

Details Continuum statistics of the Airy2 process Continuum statistics of the Airy2 process

2011-06-14

arxiv.org/abs/1106.2717v4

Mathematics

Probability

More details added, some minor mistakes corrected

Scientific paper

We develop an exact determinantal formula for the probability that the Airy$_2$ process is bounded by a function $g$ on a finite interval. As an application, we provide a direct proof that $\sup(\aip(x)-x^2)$ is distributed as a GOE random variable. Both the continuum formula and the GOE result have applications in the study of the end point of an unconstrained directed polymer in a disordered environment. We explain Johansson's [Joh03] observation that the GOE result follows from this polymer interpretation and exact results within that field. In a companion paper [MQR11] these continuum statistics are used to compute the distribution of the endpoint of directed polymers.

Affiliated with

Also associated with

No associations

Rating

Continuum statistics of the Airy2 process 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 Continuum statistics of the Airy2 process, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continuum statistics of the Airy2 process will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-113849