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- W2889859261 abstract "We establish a connection between extreme values of stable random fields arising in probability and groups G acting geometrically on CAT(-1) spaces X. The connection is mediated by the action of the group on its limit set equipped with the Patterson-Sullivan measure. Based on motivation from extreme value theory, we introduce an invariant of the action called extremal cocycle growth and show that its non-vanishing is equivalent to finiteness of the Bowen-Margulis measure for the associated unit tangent bundle U(X/G) provided X is not a tree whose edges are (up to scale) integers. As a consequence, we establish a dichotomy for the growth-rate of a partial maxima sequence of stationary symmetric $alpha$-stable ($0 < alpha < 2$) random fields indexed by groups acting on CAT(-1) spaces. We also establish analogous results for normal subgroups of free groups. This enables investigation of extremes for tree-indexed stable random fields." @default.
- W2889859261 created "2018-09-27" @default.
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- W2889859261 date "2018-09-21" @default.
- W2889859261 modified "2023-09-27" @default.
- W2889859261 title "Stable Random Fields, Bowen-Margulis measures and Extremal Cocycle Growth" @default.
- W2889859261 hasPublicationYear "2018" @default.
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