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UID:20250715T102044EDT-6585ZGj6Ec@132.216.98.100
DTSTAMP:20250715T142044Z
DESCRIPTION:Speaker: Elnur Emrah (KTH)\n\nTitle: Exit point bounds in expon
 ential last-passage percolation and a few applications\n\nAbstract:  One v
 ersatile probabilistic approach to study directed percolation and polymer 
 models is through comparison with their equilibrium versions when the latt
 er are sufficiently tractable and provide a satisfactory approximation for
  the purposes of the problem at hand. In this talk\, we focus on the parad
 igmatic setting of last-passage percolation with i.i.d. exponential weight
 s on the lattice quadrant. The equilibrium versions of this model are expl
 icitly obtained byplacing additional independent exponential weights with 
 suitable rates on the boundary (axes). Then an important aspect of the afo
 rementioned comparison scheme is to control the point where a given geodes
 ic from the origin exits the boundary. The main resultsto be presented in 
 the talk are sharp upper bounds on the tails of the exit points. While the
 se bounds can be and\, in part\, have been concurrently established via kn
 own tail bounds for the largest eigenvalue of the Laguerre ensemble\, our 
 technique is new andrelies entirely on the stationarity of the equilibrium
  models. We also aim to discuss two applications of the exit bounds relate
 d to the geometry of geodesics. These results provide upper bounds on the 
 speed of distributional convergence to the Busemann limitsand to the limit
 ing direction of the competition interface.\n\nJoint work with C. Janjigia
 n and T. Seppäläinen.\n\nLink: https://mcgill.zoom.us/j/97093259428?pwd=d2
 5yR0J6WGViSzFZOE5rT01YZnBJQT09\n\nMeeting ID: 970 9325 9428\n\nPasscode: p
 roblab\n\n \n\n \n
DTSTART:20201007T150000Z
DTEND:20201007T160000Z
SUMMARY:Elnur Emrah (KTH)
URL:/mathstat/channels/event/elnur-emrah-kth-325073
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