论塔拉格朗关于选择过程的猜想和关于正经验过程的结果 | 数学年鉴

IF 8.3 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY

ACS Applied Materials & Interfaces Pub Date : 2024-05-01 DOI:10.4007/annals.2024.199.3.6

Jinyoung Park, Huy Tuan Pham

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引用次数: 0

摘要

对于适当的高斯过程，作为大尺度定理的推论，米歇尔-塔拉格朗（Michel Talagrand，1987 年）证明了上确值明显大于其期望值的事件可以被一组其尺度之和很小的半空间所覆盖。我们证明了塔拉格朗的一个猜想，即这一结果在伯努利-$p$ 环境中的类似结果，并回答了塔拉格朗关于一般正经验过程的类似结果的问题。

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On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes | Annals of Mathematics

For appropriate Gaussian processes, as a corollary of the majorizing measure theorem, Michel Talagrand (1987) proved that the event that the supremum is significantly larger than its expectation can be covered by a set of half-spaces whose sum of measures is small. We prove a conjecture of Talagrand that is the analog of this result in the Bernoulli-$p$ setting, and answer a question of Talagrand on the analogous result for general positive empirical processes.

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来源期刊

ACS Applied Materials & Interfaces 工程技术-材料科学：综合

CiteScore

16.00

自引率

6.30%

发文量

4978

审稿时长

1.8 months

期刊介绍： ACS Applied Materials & Interfaces is a leading interdisciplinary journal that brings together chemists, engineers, physicists, and biologists to explore the development and utilization of newly-discovered materials and interfacial processes for specific applications. Our journal has experienced remarkable growth since its establishment in 2009, both in terms of the number of articles published and the impact of the research showcased. We are proud to foster a truly global community, with the majority of published articles originating from outside the United States, reflecting the rapid growth of applied research worldwide.