Universality limits for generalized Jacobi measures

Universality Limits in the Bulk for Varying Measures

Universality limits are a central topic in the theory of random matrices. We establish universality limits in the bulk of the spectrum for varying measures, using the theory of entire functions of exponential type. In particular, we consider measures that are of the form W 2n n (x) dx in the region where universality is desired. Wn does not need to be analytic, nor possess more than one derivat...

Generalized Covering Groups and Direct Limits

Generalized Universality

State machine replication reduces distributed to centralized computing. Any sequential service, modeled by a state machine, can be replicated over any number of processes and made highly available to all of them. At the heart of this fundamental reduction lies the so called universal consensus abstraction, key to providing the illusion of single shared service, despite replication. Yet, as univ...

Universality Limits at the Hard Edge of the Spectrum for Measures with Compact Support

We use the theory of entire functions and reproducing kernels to establish universality at the (hard) edge of the spectrum for a measure with compact support. This involves the Bessel kernel. In particular, we show that universality at the hard edge is equivalent to universality along the diagonal at the hard edge. 1. Results Let be a …nite positive Borel measure with compact support supp[ ]. T...

Universality Limits in the Bulk for Arbitrary Measures on Compact Sets

We present a new method for establishing universality limits in the bulk, based on the theory of entire functions of exponential type. Let be a measure on a compact subset of the real line. Assume that is absolutely continuous in a neighborhood of some point x in the support, and that 0 is bounded above and below near x, which is assumed to be a Lebesgue point of 0. Then universality holds at x...