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SUMMARY:Scaling limits of forest fire processes. - Nicolas Fournier (Marne
 -La-Vallée)
DTSTART:20110208T163000Z
DTEND:20110208T173000Z
UID:TALK28861@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:We consider the forest fire process on the integers: on each i
 nteger site\, seeds and matches fall at random\, according to some station
 ary renewal processes. When a seed falls on a vacant site\, a tree immedia
 tely grows. When a match falls on an occupied site\, a fire starts and des
 troys immediately the corresponding occupied connected component. We are i
 nterested in the asymptotics of rare fires. We prove that\, under space/ti
 me re-scaling\, the process converges (as matches become rarer and rarer) 
 to a limit forest fire process. According to the tail distribution of the 
 law of the delay between two seeds (on a given site)\, there are 4 possibl
 e limit processes. 
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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