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Gaining knowledge in a random environment

Faculty Research Seminar

Speaker: Janko Gravner, UC Davis
Related Webpage: https://www.math.ucdavis.edu/~gravner/
Location: 2112 MSB
Start time: Tue, Mar 29 2022, 12:00PM

Suppose that we have some logical statements, each represented by a vertex of a graph, and that they are all equivalent, but we are not aware of this fact.

The initial information consists of some implications, and is realized as an oriented graph. We then try to logically complete the knowledge by transitivity.

However, a capricious censor allows only certain conclusions to be made. A natural question is whether a substantial proportion of uncensored knowledge can be obtained by the transitive closure process. This simple model, on which I worked jointly with Brett Kolesnik, illustrates the use of methods from percolation theory and nucleation models.