I am a math Ph.D. student at Stanford University. I expect to receive my Ph.D. in spring 2014. My email address is jerison at stanford dot edu, and my office number is 381-A in building 380. I study probability. My advisor is Persi Diaconis.
In winter quarter 2014, I am the ACE TA for Math 51. Handouts and supplemental information from my sections are posted on this page. My office hours are Mondays 2:15-3:15 and Wednesdays 2:15-4:15.
My research is in the general area of convergence rates for Markov chains. I am interested in broadly applicable techniques that yield useful bounds on the mixing time of real-world "messy" chains lacking rigid (e.g. group) structure.
My thesis is on the method of drift and minorization. This method was developed to show exponential convergence of discrete time Markov chains on general state spaces (like subsets of R^n). It has been used to give nonasymptotic convergence bounds on chains used in Markov chain Monte Carlo estimation. I improve these quantitative bounds while providing a simpler and more probabilistic basis for the theory. In addition, my approach opens the possibility for drift and minorization arguments to yield sharp convergence rate bounds for Markov chains on finite state spaces.
In other work, I have proved a universal explicit upper bound for the mixing time of a finite Markov chain based on the absolute spectral gap and the size of the state space. See the preprint link below.
Daniel Jerison. "General mixing time bounds for finite Markov chains via the absolute spectral gap." arXiv:1310.8021 [math.PR]. (2013)
The Student Probability and Related Fields Seminar is on hiatus. The old page is here.