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University of Cambridge > Talks.cam > Trinity Mathematical Society > Uniform Bounds for Non-negativity of the Diffusion Game

## Uniform Bounds for Non-negativity of the Diffusion GameAdd to your list(s) Download to your calendar using vCal - Andrew Carlotti
- Sunday 24 February 2019, 16:55-17:30
- Winstanley Lecture Theatre, Trinity College.
If you have a question about this talk, please contact . I will discuss a variant of the chip-firing game known as the diffusion game. In the diffusion game, we begin with some integer labelling of the vertices of a graph, interpreted as a number of chips on each vertex, and then for each subsequent step every vertex simultaneously fires a chip to each neighbour with fewer chips. In general, this could result in negative vertex labels. In this talk I will answer the following question: 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-negative. I will also consider the possibility of a similar bound g(d) for each d, where d is the maximum degree of the graph. This talk is part of the Trinity Mathematical Society series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
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