Note (2/12) Other collections of open problems in probability
can be found on the web pages of
Itai Benjamini
Krzysztof
Burdzy
Tom Liggett
Ofer Zeitouni
Open problems
These problems are mostly original, and (of course) reflect my
personal taste.
But I have tried to sample different topics.
I categorize problems on a conceptual-technical spectrum.
That is
- Type 1
We have a question in words, but we don't know how to state
a precise mathematical problem
which both seems capable of solution and whose solution would be interesting.
- Type 2
We have
a precise mathematical problem,
but we do not see any plausible outline for a potential proof.
- Type 3
We have
a precise mathematical problem,
and a plausible outline for a potential proof,
but we cannot carry through the technical details.
Of course these overlap.
Continuize by taking "type 2" in the middle of an interval 1.5 - 2.5.
Then we can order the problems across this spectrum.
In a different realm, I
really
really
really
want
someone to do this simulation.
Of course, it's not easy!
Also, pages 9-12 of Lecture 3 in these
Local weak convergence of random graphs and networks lectures
give a "recursive distributional equation" I would like someone to solve numerically.
Former open problems, now solved or irrelevant.