作者：Budzinski, Thomas
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Saclay
摘要：We introduce and study a new random surface, which we call the hyperbolic Brownian plane and which is the near-critical scaling limit of the hyperbolic triangulations constructed by Curien (Probab Theory Relat Fields 165(3):509-540, 2016). The law of the hyperbolic Brownian plane is obtained after biasing the law of the Brownian plane of Curien and Le Gall (J Theoret Probab 27(4):1249-1291, 2014) by an explicit martingale depending on its perimeter and volume processes studied by Curien and Le...
作者：Collins, Benoit; Dahlqvist, Antoine; Kemp, Todd
作者单位：Kyoto University; Centre National de la Recherche Scientifique (CNRS); University of Cambridge; University of California System; University of California San Diego
摘要：The Brownian motion on the unitary group converges, as a process, to the free unitary Brownian motion as . In this paper, we prove that it converges strongly as a process: not only in distribution but also in operator norm. In particular, for a fixed time , we prove that the unitary Brownian motion has a spectral edge: there are no outlier eigenvalues in the limit. We also prove an extension theorem: any strongly convergent collection of random matrix ensembles independent from a unitary Brown...
