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SUMMARY:mini-course: An introduction to supersymmetry and the vertex-reinf
 orced jump process - Silke Rolles (Technische Universität München)\, Fra
 nz Merkl (Ludwig-Maximilians-Universität München)
DTSTART:20240829T090000Z
DTEND:20240829T110000Z
UID:TALK219772@talks.cam.ac.uk
DESCRIPTION:In this minicourse\, we introduce and relate two closely conne
 cted models\, the nonlinear supersymmetric hyperbolic sigma model on the o
 ne hand and the vertex-reinforced jump process on the other hand.\nTo prep
 are the study of the first model\, an introduction to supersymmetry will a
 lso be given\, which deals with both\, commuting and anticommuting variabl
 es with values in a Grassmann algebra\, and first order linear differentia
 l operators mixing them.\nThe first model is then a statistical mechanics 
 type spin model with spin components taking values in this Grassmann algeb
 ra.\nThe second model is a stochastic process for a particle with memory j
 umping in continuous time on agraph. The memory is encoded in the local ti
 mes the particle has already spent at the vertices of the graph\; frequent
 ly visited sites have a larger rate to be visited again.&nbsp\; Asymptotic
  ratios of local times of the second model have a direct interpretation in
  terms of spin variables of the first model in appropriate coordinates.\nW
 e explain some bounds in the first model and show how they can be used to 
 understand the recurrence and transience behaviour in the second model.\nT
 he minicourse includes some joint work with Margherita Disertori and Pierr
 e Tarr&egrave\;s.
LOCATION:Seminar Room 2\, Newton Institute
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