4 papers
New simple proofs of the Kolmogorov extension theorem and Prokhorov's theorem
Wooyoung Chin
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 $\ma…
A note on invariance of the Cauchy and related distributions
Wooyoung Chin, Paul Jung, Greg Markowsky
It is known that if is an analytic self map of the complex upper half-plane which also maps to itself, and , then preserves the Cauchy di…
An Exposition on Wigner's Semicircular Law
Wooyoung Chin
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…
A Probabilistic Proof of a Wallis-type Formula for the Gamma Function
Wooyoung Chin
We use well-known limit theorems in probability theory to derive a Wallis-type product formula for the gamma function. Our result immediately provides a probabilistic proof of Wall…