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We consider a Poisson hail on an infinite d-dimensional ground. In other words, there is a Poisson rain of “hailstones” of a random size (height+width). In the case of a cold ground, we analyze conditions for at most linear growth. In the case of a hot ground (hailstones are melt when touch the ground), we are interested in stability conditions. In the case of a mixed ground, we look at the shapes of growth.
Professor Foss received PhD (1982) and DSc (1992) in Probability Theory and Mathematical Statistics from Novosibirsk State University. He was a Professor at NSU in 1982-1996, and a Leading Research Scientist at Sobolev Institute of Mathematics in Novosibirsk in 1996-2000. Since 2000 he is a Professor of Applied Probability at Heriot-Watt University, Edinburgh, UK. Professor Foss main research interests are in applied probability, stochastic processes, queueing theory, stability and performance of stochastic systems, heavy-tailed distributions, spatial models. He published extensively in leading probability and applied probability journals, and is an author of four books. His research has been supported by numerous grants from European agencies. He currently serves as Editor-in-Chief of Queueing Systems, and as Associate Editor of the Journal of / Advances in Applied Probability, and Markov Processes and Related Fields.