We prove the edge universality of the beta ensembles for any β > 1, provided that the limiting spectrum is supported on a single interval, and the external potential is C 4 and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to ...

The topic of lepton universality is directly related to the structure of the fundamental fermion elds and the dynamics generating it. It can be investigated independently for the charged and the neutral weak interactions. The precise measurements of the neutral couplings achieved at LEP and SLC are the key ingredients for the investigation of electroweak radiative corrections and the indirect i...

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...

In order to have a better understanding of finite random matrices with non-Gaussian entries, we study the 1/N expansion of local eigenvalue statistics in both the bulk and at the hard edge of the spectrum of random matrices. This gives valuable information about the smallest singular value not seen in universality laws. In particular, we show the dependence on the fourth moment (or the kurtosis...

We prove that de Branges spaces of entire functions describe universality limits in the bulk for random matrices, in the unitary case. In particular, under mild conditions on a measure with compact support, we show that each possible universality limit is the reproducing kernel of a de Branges space of entire functions that equals a classical Paley-Wiener space. We also show that any such repro...

For certain classes of systems operating at a critical point, the concept of universality can offer a way out of the reductive dilemma of modeling systems with many interacting parts. In these cases, simple models can be used to classify the large scale behavior of an entire universality class. This paper provides a brief introduction to the idea of universality and the renormalization group id...