Need advice on choosing probability PhD programs.

[Taxxi]

Hello, everyone. My main interest is probability and analysis PhD programs, but as an international student I am having a hard time choosing which university offers good program related to probability theory (and statistics along the way). What I know is that some of the research is in conjunction with combinatorics and some go along the path of stochastic calculus. In short, I want to get some advice to the following questions of mine:

• Which university offers strong PhD program related to probability theory? What I know is that most of the top 10 schools offer great programs, but I am also wondering what other universities have good program in probability other than the top 10s for reaches and safer choices.

• Which university offers a great degree of freedom regarding the fields I can study? I also wish choosing the advisor is flexible. As most applicants, I'm not firmly decided on my research field and I have a huge interest in nonstandard analysis and differential geometry as well(though I got a very bad grade in the subject due to some reasons...) As far as I can see, Cornell offers diverse opportunities by offering three faculty members to one student, and they can be changed as I progress and my subject of interest is changed. I want to know more universities with such flexibility.

• Which university do you think is a reach and a safe bet for my profile listed below? I am mainly thinking of applying for probability at the moment. Or do you think I should opt for statistics as well?

• Should I pre-contact some of the potential advisors? There are some researching areas I am interested but I doubt I am qualified to make a good comment about it.

Undergrad Institution: Top 3 in my country.
Majors: Mathematics, Economics.
GPA: 3.76/4.0
Type of Student: International (Asian)
Awards/Honors: Graduated with High Honors. Bunch of honors and scholarships (within the university).
Math/Statistics Grades: Mostly got As. Took some statistics classes as well(mathematical statistics, Bayesian statistics). Also took stochastic process but received B+. Not bad in analysis but very strong in algebra including mathematical logic and algebraic combinatorics.

GRE General Test: 166V, 169Q, 4.5W.
GRE Subject Math Test: Waiting for the result. Expecting higher than 90% minimum.
Programs Applying: Probability.

Research Experience: None...
Working Experience: Quantitative researcher in a fintech startup company (1 year). My researching area was asset allocation with weight constraints, and I actually implemented the program using quadratic programming in Python. Working experience in Python and ML. Developed several low frequency trading algorithms. I have done so much since it was a small startup, working with a statistician in finance(Master) and a mathematician(PhD, probability and PDE).
Hobbies: Analyzing old classics games, finding the optimal strategy using probability theory and sometimes Python. Fun stuff. This is what got me the job.
Letters of Recommendation: I doubt they will be particularly strong but I doubt they will be detrimentally bad either. 1 from my set theory and mathematical logics professor, 1 from my linear algebra and abstract algebra professor, and 1 from my probability professor.



Thank you in advance sincerely for your advice.

[Sampaoli]

I don't know about your chances in each of these programs but the top probability programs in the US are :

1st tier:

- Courant
- MIT

then

- Stanford
- Chicago
- Northwestern
- Minnesota
- Washington

2nd tier:

- Berkeley
- Wisconsin
- Cornell (traditional place for prob. 20y ago)
- Utah
- UCLA
- CUNY
- Columbia
- UPenn

3rd tier:

- UVA
- TAMU
- UIUC
- GeorgiaTech
- UCSD


I am not including Harvard (H.T. Yau) and Princeton (Sly) since they provide only one option of a potential advisor. Of course these two are great schools in any case.

[Taxxi]

@Sampaoli I wish someone had helped me sooner... it is too late to incorporate these universities. Still thank you for your providing information.

[Junaid456]

I don't know about your chances in each of these programs but the top probability programs in the US are :

1st tier:

- Courant
- MIT

then

- Stanford
- Chicago
- Northwestern
- Minnesota
- Washington

2nd tier:

- Berkeley
- Wisconsin
- Cornell (traditional place for prob. 20y ago)
- Utah
- UCLA
- CUNY
- Columbia
- UPenn

3rd tier:

- UVA
- TAMU
- UIUC
- GeorgiaTech
- UCSD


I am not including Harvard (H.T. Yau) and Princeton (Sly) since they provide only one option of a potential advisor. Of course these two are great schools in any case.

I'm also applying for probability at applied math and statistics schools. Are all these programs pure math programs on your list. I am also an international applicant so I am looking to aim high but apply widely at the same time to have a decent shot at the middle tier. Any suggestions for applied math/statistics programs with probability people. Getting into a top pure math program is not going to be easy.