- gauge feasibility for certain schools in the US; and
- further build the list of research areas or places in the US that I'm considering.

Research areas

I am interested in probability theory, applied probability, stochastic processes, and the more theoretical side of statistics. Examples of areas of interest (in no particular order):

- extreme value theory or heavy-tailed distributions
- time series
- Bayesian nonparametrics
- information theory
- survival analysis

I have done some analysis (real analysis/complex analysis/topology/metric spaces/measure theory) — maybe above average for Statistics PhD applicants but below average for Mathematics PhD applicants — and am particularly open to research areas that rely on analysis/measure theory. I notice that mathematical physics seems to inspire a lot of probability research in the US; I am completely unfamiliar with how probability is used there and as a result am not so interested (yet).

Places

I have gathered the following list of places in the US I might consider (mainly inspired by particular members of faculty but sometimes by general faculty strength):

- Cornell — Operations Research and Information Engineering
- Columbia — Statistics
- Duke — Statistics
- Stanford — Statistics
- Stanford — Management Science and Engineering
- UC Davis — Statistics
- UC San Diego — Mathematics
- Yale — Statistics
- UNC at Chapel Hill — Statistics and Operations Research
- UC Santa Barbara — Statistics and Applied Probability

I have to confess that I have not looked closely at mathematics departments, because I think my chances at admission are slim there compared to statistics.

Profile

Institution: One of the top Australian universities (same institution for both undergrad and masters)

Major(s): Probability Theory

Minor(s): Statistics, Actuarial Science

GPA: Not the scale we use but should be > 3.9/4.0

Type of Student: International Asian male

GRE Revised General Test: Not sat yet

GRE Subject Test in Mathematics: Not sat yet

Research Experience: Masters thesis resulted in a preprint. 4-week undergrad project on fractional Brownian motion (very out of my league at the time).

Awards/Honors/Recognitions: Top MSc student among those specialising in probability or statistics (probably 60+ students).