Lectures on the mean values of functionals -- An elementary introduction to infinite-dimensional probability

2017/05/10 by Cheng-shi Liu, Liu, Cheng-shi
Mathematics · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Probability (math.PR) #Probability and Statistical Research #Statistical Mechanics and Entropy #Statistics Theory (math.ST) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1705.03584

openalex publication_date 2017/05/10 · openalex created_date 2017/05/19 · openalex updated_date 2026/07/28

Abstract

This is an elementary introduction to infinite-dimensional probability. In the lectures, we compute the exact mean values of some functionals on C[0,1] and L[0,1] by considering these functionals as infinite-dimensional random variables. The results show that there exist the complete concentration of measure phenomenon for these mean values since the variances are all zeroes.

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