Brownian motion model of random matrices revisited

Details Brownian motion model of random matrices revisited Brownian motion model of random matrices revisited

1998-04-23

arxiv.org/abs/cond-mat/9804253v1

Physics

Condensed Matter

3 pages, LaTeX

Scientific paper

We present a modified Brownian motion model for random matrices where the eigenvalues (or levels) of a random matrix evolve in "time" in such a way that they never cross each other's path. Also, owing to the exact integrability of the level dynamics, we incorporate long-time recurrences into the random walk problem underlying the Brownian motion. From this model, we derive the Coulomb interaction between the two eigenvalues. We further show that the Coulomb gas analogy fails if the confining potential, $V(E)$ is a transcendental function such that there exist orthogonal polynomials with weighting function, $\exp [-\beta E]$, where $\beta $ is a symmetry parameter.

Affiliated with

Also associated with

No associations

Rating

Brownian motion model of random matrices revisited 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 Brownian motion model of random matrices revisited, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Brownian motion model of random matrices revisited will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-672247