50 years of first passage percolation
By Antonio Auffinger, Michael Damron, Jack Hanson. 2015
279 citations recorded by the source corpus.
We celebrate the 50th anniversary of one the most classical models in probability theory. In this survey, we describe the main results of first passage percolation, paying special attention to the recent burst of advances of the past 5 years. The purpose of these notes is twofold. In the first chapters, we give self-contained proofs of seminal results obtained in the '80s and '90s on limit shapes and geodesics, while covering the state of the art of these questions. Second, aside from these classical results, we discuss recent perspectives and directions including (1) the connection between Busemann functions and geodesics, (2) the proof of sublinear variance under 2+log moments of passage times and (3) the role of growth and competition models. We also provide a collection of (old and new) open questions, hoping to solve them before the 100th birthday.
Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/4fc808dca23bb4112ce197a048167a73182fb698
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Citations in the corpus
- Random Growth Models (2018, background): “…Board Suncica Canic Tasso J. Kaper (Chair) Daniel Rockmore LECTURE NOTES PREPARED FOR THE AMERICAN MATHEMATICAL SOCIETY SHORT COURSE ON RANDOM GROWTH MODELS HELD IN ATLANTA, GEORGIA, JANUARY 2–3, 2017 The AMS Short Course Series is sponsored by the Society’s Program Committee for National Meetings.”