2018/10/31 by Erik Bates, Sourav Chatterjee · 1 citation
Mathematics · #math.PR #msc:60E15 #msc:60K35 #msc:82D60 #msc:60K37
published as Ann. de l'Inst. Henri Poincare Probab. Stat. (2020), Vol. 56, no. 4, 2406-2427 · 24 pages, 1 figure. Minor edits in this revision
arxiv created 2021/08/26 · arxiv updated 2021/08/30
We prove √(log n) lower bounds on the order of growth fluctuations in three planar growth models (first-passage percolation, last-passage percolation, and directed polymers) under no assumptions on the distribution of vertex or edge weights other than the minimum conditions required for avoiding pathologies. Such bounds were previously known only for certain restrictive classes of distributions.In addition, the first-passage shape fluctuation exponent is shown to be at least 1/8, extending previous results to more general distributions.