𝔖 Bobbio Scriptorium
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Random disease on the square grid

✍ Scribed by József Balogh; Gábor Pete

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
197 KB
Volume
13
Category
Article
ISSN
1042-9832

No coin nor oath required. For personal study only.

✦ Synopsis

We introduce some generalizations of a nice combinatorial problem, the central notion of which is the so-called Disease Process. Let us color independently each Ž . square of an n = n chessboard black with a probability p n ; this is a random initial configuration of our process. Then we have a deterministic painting or expansion rule, and the question is the behavior of the disease process determined by this rule of spreading. In Ž . particular, how large must p n be to paint the whole chessboard black? The main result of this paper is the almost exact determination of the threshold function in the fundamental case of this Random Disease Problem. We include further investigations into the general randomized and deterministic cases.

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