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SUMMARY:The bead process on the torus - Samuel Johnston (King's College Lo
 ndon)
DTSTART:20230502T130000Z
DTEND:20230502T140000Z
UID:TALK200479@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Consider the semi-discrete torus T_n := [0\, 1) × {0\, 1\, . 
 . . \, n − 1} representing n unit length strings running in parallel. A 
 bead configuration is a point process on T_n with the property that betwee
 n every two consecutive points on the same string\, there lies a point on 
 each of the neighbouring strings. \n\nWe develop a continuous version of K
 asteleyn theory to show that partition functions for bead configurations o
 n T_n may be expressed in terms of Fredholm determinants of certain operat
 ors on T_n\, and thereby obtain an explicit formula for the volume of bead
  configurations. The asymptotics of this volume formula confirm a recent p
 rediction of\nShlyakhtenko and Tao in the free probability literature. \n\
 nThereafter we study random bead configurations on T_n\, making connection
 s with exclusion processes and providing a\nnew probabilistic representati
 on of TASEP on the ring.\n
LOCATION:MR12\, Centre for Mathematical Sciences
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