Profile Eval/Program suggestions

[Probably Probability]

Hello,

I am considering applying to PhD programs in either OR or statistics .  I have a few questions about my background and PhD programs.

I am a double major in math and business economics from a flagship R1 university (but not super selective), with an overall gpa of about 3.89.  My math major gpa is about 3.97. I have an A- in one math class (intro analysis) and A’s in the rest (linear algebra, intro analysis 2, differential equations, two statistical inferences classes(senior level/graduate), measure theoretic probability(PhD level), two undergrad/masters and one PhD stochastic processes classes, optimization(senior level/graduate, very rigorous with mainly PhD students), math modeling (Senior level/Graduate), and real analysis(class mainly focused on topology, measure and integration, and functional analysis)).  I have a few A-‘s and B+‘s in some of my gen eds and more discussion based econ classes, but have A’s in game theory and econometrics (3 classes).   I have no grades below a B+.  I have taken a class on OOP in Java.  I am best at R, but know some python and Java.

I am currently an economics research assistant and a fairly prestigious institution.  In my undergrad, I was a research assistant for a game theory professor and a teaching assistant for econometrics. I have had a couple analytics internships.

I really enjoy stochastic processes and probability and would like to do probability research or probability modeling.  I also really enjoy game theory and am curious about mechanism design.  I am also curious about decision theory and risk analysis, as I really enjoy the topics on expected utility theory from micro.  These are the topics I would probably plan to study in an OR PhD.

But I also really enjoy the pure side of probability, and am considering phd in statistics with a focus on probability ( maybe a math PhD, but I am unsure if I would be a competitive candidate since I don’t have much pure math experience).  I would also consider statistics as a research topic, but I am only really familiar with my statistical inference and econometrics.

Are there any classes I should take to fill any gaps? I am considered taking a class on algorithms or a topology class (my work will pay for it).  Or maybe take some PhD level mathematical statistical theory classes.

I am planning to take GRE soon.  Based on practice sets, I believe I can score pretty high on the quant section.

What PhD programs should I aim for? Do I have a chance at a top 20 program? Of course that will depend heavily on LORs (my measure theoretic probability Professor agreed to write me one), but do I have a sufficient background?   I do plan to apply to a wide range of schools.

What are some good schools for probability that aren’t super competitive like MIT or NYU?  I know lots of probability schools are housed in math departments but due to my experience and coursework, I think I would do better in a statistics or an OR PhD.

Some programs I have been researching are:

UNC STOR (Probability Focus)

Duke Decision Science (Applied Probability, Decision Theory, Mechanism Design)

NC State OR (Stochastic Processes, Decision Theory)

Michigan State Statistics (Probability Track)

UCSB Statistics (Probability Focus)

I have been looking at a lot more but these seem to fit my criteria as: A)Operations Research department with good probability and/or micro theory. b) Statistics departments with probability focus.