Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, December 1, 2020.

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Tuesday, December 1, 2020

2:00 pm in Zoom,Tuesday, December 1, 2020

Prague dimension of random graphs

Lutz Warnke (Georgia Institute of Technology)

Abstract: In the 1970s, Nesetril, Pultr and Rodl introduced the Prague dimension of graphs, which is related to clique edge coverings. Proving a conjecture of Furedi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order $n/log n$ for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities, i.e., edges of size $O(log n)$.

For Zoom information please contact Sean at SEnglish (at) illinois (dot) edu.

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Tuesday, December 1, 2020

Joint distribution of Busemann functions in corner growth models

Wai-Tong (Louis) Fan (Indiana University)

Abstract: The 1+1 dimensional corner growth model with exponential weights is a centrally important exactly solvable model in the Kardar-Parisi-Zhang class of statistical mechanical models. While significant progress has been made on the fluctuations of the growing random shape, understanding of the optimal paths, or geodesics, is less developed. The Busemann function is a useful analytical tool for studying geodesics. We present the joint distribution of the Busemann functions, simultaneously in all directions of growth, in terms of mappings that represent FIFO (first-in-first-out) queues. As applications of this description we derive a marked point process representation for the Busemann function across a single lattice edge and point out its implication on structure of semi-infinite geodesics. This is joint work with Timo Seppäläinen.