Some notes for arguably the most powerful trace inequality $\text{tr}\exp(A+B)\le \text{tr} \exp(A)\exp(B)$.
"Sarcasm is the lowest form of wit but the highest form of intelligence" - Oscar Wilde.
"No betting system can convert a subfair game into a profitable enterprise..." — Probability and Measure (second edition, page 94) by Patrick Billingsley.
“People who wish to analyze nature without using mathematics must settle for a reduced understanding.” — Richard P. Feynman
At one point, I wanted to know how Black-Scholes formula is used in practice. The bottom line is that B-S formula is in some sense, "BS" (many of the assumptions are too hopeful); however, it does provide an estimate for the true prices. Read more
arXiv Probability Preprints
Probability Recommended
Gaussian Processes
I'm pursuing a PhD in Mathematics at Penn State. The purpose of this website is to record my research activities, mathematical notes, teaching materials, and some tutorials. More information and how to navigate my website will be in the Personal page.
Favorite quote by Paul Erdős about Ramsey numbers:
Imagine an alien force, vastly more powerful than us landing on Earth and demanding the value of $R(5, 5)$ or they will destroy our planet. In that case, we should marshal all our computers and all our mathematicians and attempt to find the value. But suppose, instead, that they asked for $R(6, 6)$, we should attempt to destroy the aliens.
PhD in Mathematics, 2016-present
Pennsylvania State University
BSc in Mathematics, 2012-2016
University of Texas at San Antonio
Some notes for arguably the most powerful trace inequality $\text{tr}\exp(A+B)\le \text{tr} \exp(A)\exp(B)$.
MATH 22