Is probability a well-established field without room to grow? As I pursue my PhD in statistical science, I have grown very fond of probability theory.  I was curious if it was worth furthering my background in probability past more advanced topics such as: Brownian Motion, Donsker's invariance principle, etc. in hopes of somehow offering something to the field.  I also would like to find areas of intersection such as statistical physics or network theory/reinforcement learning.
Is probability advancing anymore or is it a well-established field without much room to grow?
 A: I would divide the answer into two parts.
Examination whether probability is the right measure of uncertainty 


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*E.g. relation to Dampster-Shaffer theory


Theories on probabilistic X where X may stand for


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*Probabilistic Model Checking 

*Fully Probabilistic Design 

*Probabilistic Inference

*Probabilistic Automata

*Deep Probabilistic Programming


If you are interested in more details, search for the keywords (e.g. scholar.google.com ) and focus on results in last few years.
A: There are a number of academic journals devoted only to publishing new findings in probability, and they are thriving. And there are many other journals devoted to publishing new findings in mathematics that include among other things probability.
Take a look at this page. At the beginning of the semester this might not yet have much, but follow it from week to week and you will see speakers presenting their new results in probability theory. Do the same at any of many other universities and you see the same thing.
