High-dimensional Lipschitz functions are typically flat
نویسندگان
چکیده
منابع مشابه
Lipschitz Functions on Expanders are Typically Flat
This work studies the typical behavior of random integer-valued Lipschitz functions on expander graphs with sufficiently good expansion. We consider two families of functions: M -Lipschitz functions (functions which change by at most M along edges) and integer-homomorphisms (functions which change by exactly 1 along edges). We prove that such functions typically exhibit very small fluctuations....
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A grounded M -Lipschitz function on a rooted d-ary tree is an integer-valued map on the vertices that changes by at most M along edges and attains the value zero on the leaves. We study the behavior of such functions, specifically, their typical value at the root v0 of the tree. We prove that the probability that the value of a uniformly chosen random function at v0 is more than M + t is doubly...
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In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire’s category) have a maximal Clarke subdifferential. In the present paper, we show that in a separable Banach space the set of non-expansive Lipschitz functions with a maximal Clarke subdifferential is not only of generic, but also staunch. 1991 Mathematics Subject Classification: Primary 49J52.
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2017
ISSN: 0091-1798
DOI: 10.1214/16-aop1089