Theory of Probability and Random Processes

Abstract

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Makhtesh Ramon Complex Deposit (Southern Israel) – A Window to the Upper Mantle

“…Actually, significance of mineralogical indicator (revealing of diamonds and indicator minerals) is greatly high than ½. The probability of the random coincidence of these factors (according to the trivial rules of the probability theory (e.g., Koralov and Sinai, 2007)) in this case is (½) 6 = 0.0156=1.56%, e.g. positive assessment of the diamond-bearing of Makhtesh Ramon area is 98.44%.…”

Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation

“…See The assumption (1.1) with v α = O(L α∧2 ) indeed holds if, e.g., h(x) ∼ c|x| −d−α as |x| → ∞ for some constant c (see [7,Section 10.5] for the 1-dimensional case). Let…”

Optimal vaccination strategies and rational behaviour in seasonal epidemics

“…Let p n ∈ C + ([0, T ]) be such that p n → p ∈ RM + , in the weak topology, cf. (Koralov and Sinai, 2007), and let…”