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SUMMARY:Uniform Bounds for Non-negativity of the Diffusion Game - Andrew C
 arlotti
DTSTART:20190224T165500Z
DTEND:20190224T173000Z
UID:TALK120799@talks.cam.ac.uk
CONTACT:73969
DESCRIPTION:I will discuss a variant of the chip-firing game known as the 
 diffusion game. In the diffusion game\, we begin with some integer labelli
 ng of the vertices of a graph\, interpreted as a number of chips on each v
 ertex\, and then for each subsequent step every vertex simultaneously fire
 s a chip to each neighbour with fewer chips. In general\, this could resul
 t in negative vertex labels. In this talk I will answer the following ques
 tion: do there exist values f(n)\, for each n\, such that whenever we have
  a graph on n vertices and an initial allocation with at least f(n) chips 
 on each vertex\, then the number of chips on each vertex will remain non-n
 egative. I will also consider the possibility of a similar bound g(d) for 
 each d\, where d is the maximum degree of the graph.
LOCATION:Winstanley Lecture Theatre\, Trinity College
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