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UID:20251008T145136EDT-3165sgSVpO@132.216.98.100
DTSTAMP:20251008T185136Z
DESCRIPTION:Title: The KPZ scaling limit of the colored asymmetric simple e
 xclusion process.\n\nAbstract: In the colored asymmetric simple exclusion 
 process (ASEP)\, one places a particle of 'color' -k at each integer site 
 k ∈ \Z. Particles attempt to swap places to the left with rate q ∈ [0\,1) 
 and to the right with rate 1\; the swap succeeds if the initiating particl
 e has a higher color than the other particle (thus the particles tend to g
 et more ordered over time). We will discuss the space-time scaling limit o
 f this process (as well as a related discrete analog known as the stochast
 ic six-vertex model)\, captured via a height function given by certain col
 ored particle counts. The limit lies in the Kardar-Parisi-Zhang universali
 ty class\, and is given by the Airy sheet and directed landscape\, which w
 ere first constructed in 2018 by Dauvergne-Ortmann-Virág as limits in a ve
 ry different setting---of a model of a random directed metric. The Yang-Ba
 xter equation and line ensembles (collections of random non-intersecting c
 urves) with certain Gibbs or spatial Markov properties will play fundament
 al roles in our discussion. Joint work with Amol Aggarwal and Ivan Corwin.
 \n\n \n
DTSTART:20240229T163000Z
DTEND:20240229T173000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Milind Hegde (Columbia University)
URL:/mathstat/channels/event/milind-hegde-columbia-uni
 versity-355708
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