2004/06/07 by Andrzej Czygrinow, Czygrinow, Andrzej, Glenn Hurlbert +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #05A20 #05C35 #05D05 #Combinatorics (math.CO) #FOS: Mathematics #Quantum chaos and dynamical systems #Random Matrices and Applications #Stochastic processes and financial applications #math.CO #msc:05A20 #msc:05C35 #msc:05D05
paper · pdf · doi:10.48550/arxiv.math/0406124
8 pages, preliminary version
arxiv created 2004/06/07 · openalex publication_date 2004/06/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A configuration of pebbles on the vertices of a graph is solvable if one can place a pebble on any given root vertex via a sequence of pebbling steps. A function is a pebbling threshold for a sequence of graphs if a randomly chosen configuration of asymptotically more pebbles is almost surely solvable, while one of asymptotically fewer pebbles is almost surely not. In this note we show that the spectrum of pebbling thresholds for graph sequences spans the entire range from n1/2 to n. This answers a question of Czygrinow, Eaton, Hurlbert and Kayll. What the spectrum looks like above n remains unknown.