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Showing 1 to 7 of 7 for “"metric measure spaces"”.
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Extensions of the theory of tent spaces and applications to boundary value problems
We extend the theory of tent spaces from Euclidean spaces to various types of metric measure spaces. For doubling spaces we show that the usual 'global' theory remains valid, and for 'non-uniformly locally doubling' spaces (including R^n with the Gaussian measure) we establish a satisfactory local …
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Extensions of the theory of tent spaces and applications to boundary value problems
We extend the theory of tent spaces from Euclidean spaces to various types of metric measure spaces. For doubling spaces we show that the usual 'global' theory remains valid, and for 'non-uniformly locally doubling' spaces (including R^n with the Gaussian measure) we establish a satisfactory local …
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A tensor product approach to non-local differential complexes
… complexes of Alexander-Spanier type on metric measure spaces associated with (generally) unbounded non-local operators, such as operators of fractional Laplacian type. We show that these complexes can be used to approximate complexes of differential forms in a non-local-to-local …
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Liouville Properties and Dimensionality Bounds for Harmonic and Caloric Functions
… we study several Liouville properties in geometric analysis. First, we prove a Hamilton type and a Souplet-Zhang type gradient estimates which imply a strong Liouville theorem for ancient f-caloric functions with certain growth assumption on smooth metric measure spaces. Second, we generalize …
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On the metric structure of random planar maps and SLE-decorated Liouville quantum gravity
… statistical mechanics models on them) viewed as metric measure spaces equipped with the graph distance and the counting measure on vertices. In particular, we show that uniform random planar maps (which correspond to the case [gamma]= [square root of]8/3) decorated by a self-avoiding walk or a …
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Algorithmic randomness on computable metric spaces and hyperspaces
… generalizing Martin-Löf randomness to computable metric spaces with arbitrary measure (for examples of this type of generalization see Gács [14], Rojas and Hoyrup [15]. The aim of this generalization is to define algorithmic randomness on the hyperspace of non-empty compact subsets of a computable …
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New Directions in Bandit Learning: Singularities and Random Walk Feedback
… In Chapter 2, I study bandit learning problem in metric measure spaces. I start with multi-armed bandit problem with Lipschitz reward, and propose a practical algorithm that can utilize greedy tree training methods and adapts to the landscape of the reward function. In particular, the study …