Status  Confirmed 
Seminar Series  LPTMS 
Subjects  condmat.statmech 
Date  Tuesday 3 October 2023 
Time  11:00 
Institute  LPTMS 
Seminar Room  Salle des séminaires du FAST et du LPTMS, bâtiment Pascal n°530 
Speaker's Last Name  Boyer 
Speaker's First Name  Denis 
Speaker's Email Address  
Speaker's Institution  Universidad Nacional Autónoma de México 
Title  Optimising the random search of a target with finite lifetime 
Abstract  Random searches find applications in a broad range of problems in biology, chemistry or everyday life. In a typical setup, a searcher follows a random motion and reacts with a fixed target site upon first encounter. In many situations, however, the target has a finite lifetime after which it becomes inactive, lost or no longer available for reaction. To be successful, the searcher must therefore find the target site before the latter becomes inactive. We present exact results on a minimal model, namely, a onedimensional searcher performing a discrete time random walk or Lévy flight, while the target has an exponentially distributed lifetime. In contrast with the case of a permanent target, it is possible to optimise the capture probability and the conditional mean first passage time at the target. The optimal Lévy index takes a nontrivial value, even by taking the infinite lifetime limit, and exhibits a "phase transition" as the initial distance to the target site is varied. This transition can be discontinuous or continuous depending on the target lifetime. We outline connections between this problem and search processes based on resetting. 
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