Abstract
We discuss Derrida’s random energy models under the light of the recent advances in the study of the extremes of highly correlated random fields. In particular, we present a refinement of the second moment method which provides a unifying approach to models where multiple scales can be identified, such is the case for e.g. branching diffusions, the 2-dim Gaussian free field, certain issues of percolation in high dimensions, or cover times. The method identifies some universal mechanisms which seemingly play a fundamental role also in the behavior of the extremes of the characteristic polynomials of certain random matrix ensembles, or in the extremes of the Riemann ζ-function along the critical line.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
