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UID:0-991@lptms.universite-paris-saclay.fr
DTSTART;TZID=Europe/Paris:20250128T110000
DTEND;TZID=Europe/Paris:20250128T120000
DTSTAMP:20250118T150646Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-du-lptm
 s-joseph-baron-bath-uk/
SUMMARY:Séminaire du LPTMS : Joseph Baron (University of Bath) - Salle des
  séminaires du FAST et du LPTMS\, bâtiment Pascal n°530 - 28 Jan 25 11:
 00
DESCRIPTION:Perturbative and non-perturbative approximation schemes for spa
 rse random matrices\nJoseph Baron (University of Bath)\n\nRandom matrix th
 eory (RMT) has proved an invaluable tool for the study of systems with dis
 ordered interactions in many quite disparate research areas. Widely applic
 able results\, such as the celebrated elliptic law for dense random matric
 es\, allow one to understand when stability is possible in well-connected 
 many-component dynamical systems\, for instance. However\, such simple and
  universal results have been more difficult to come by in the case of spar
 se random matrices\, for which the average number of non-zero entries per 
 row (p) is small compared to the matrix size (N). This is despite the fact
  that sparsity is a common feature of interaction networks in many applica
 tions.\n\nIn this talk\, I will discuss the two ways in which the spectra 
 of sparse random matrices deviate from the classic elliptic law\, and I wi
 ll present approximation schemes that allow us to characterise these novel
  features analytically. (1) I will show how diagrammatic series can be use
 d to understand the 1/p corrections to the elliptic law. A simple closed-f
 orm expression for the "warped ellipse"\, to which most of the eigenvalues
  are confined\, is derived. (2) I will also demonstrate how a cavity appro
 ach can be used to characterise the Lifshitz tails of the spectrum. We wil
 l see that eigenvalues in these tail regions of the spectrum correspond to
  abnormally well-connected hubs of the network (which the random matrix re
 presents)\, and that the corresponding eigenvectors are exponentially loca
 lised around these hubs.
CATEGORIES:seminars
LOCATION:Salle des séminaires du FAST et du LPTMS\, bâtiment Pascal n°53
 0\, rue André Riviere\, Orsay\, 91405\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=rue André Riviere\, Orsay\
 , 91405\, France;X-APPLE-RADIUS=100;X-TITLE=Salle des séminaires du FAST 
 et du LPTMS\, bâtiment Pascal n°530:geo:0,0
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