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Wooyoung Chin

Publications and source records attributed to Wooyoung Chin.

4 recordsLinked to original sources
arXiv2019

New simple proofs of the Kolmogorov extension theorem and Prokhorov's theorem

We provide new simple proofs of the Kolmogorov extension theorem and Prokhorovs' theorem. The proof of the Kolmogorov extension theorem is based on the simple observation that $\mathbb{R}$ and the product measurable space $\{0,1\}^\mathbb{N}$ are Borel isomorphic. To show Prokhorov's theorem, we observe that we can assume that the underlying space is $\mathbb{R}^\mathbb{N}$. Then the proof of Prokhorov's theorem is a straightforward application of the Kolmogorov extension theorem we just proved.

math.PR↗
arXiv2019

A note on invariance of the Cauchy and related distributions

It is known that if $f$ is an analytic self map of the complex upper half-plane which also maps $\mathbb{R}\cup\{\infty\}$ to itself, and $f(i)=i$, then $f$ preserves the Cauchy distribution. This note concerns three results related to the above fact.

math.PR↗
arXiv2019

An Exposition on Wigner's Semicircular Law

We revisit the moment method to obtain a slightly strengthened version of the usual semicircular law. Our version assumes only that the upper triangular entries of Hermitian random matrices are independent, have mean zero and variances close to $1/n$ in a certain sense, and satisfy a Lindeberg-type condition. As an application, we derive another semicircular law for the case when the sum of a row converges in distribution to the standard normal distribution, including the case where all matrix entries may have infinite variance. The appendix, making up the majority of the paper, provides for those new to the subject, a rigorous exposition of most details involved, including also a proof of a semicircular law that uses the Stieltjes transform method.

math.PR↗