This collection was started as this 2003 PDF document and became a web site around 2006. To maintain a historical record I have not deleted any pages. I update rather haphazardly, but may not have noted all current relevant work. So let me know anything that should be added.

These problems are mostly original, and (of course) reflect my personal taste. They are definitely not intended as the most important open problems in Probability, and I do not follow the most active current research areas. Historically I have emphasised problems that seem conceptually somewhat novel, rather than "natural next step" problems suggested by a specific known result. But upon retirement (2018) I am adding some of the latter.

Open research problems

I categorize problems on a conceptual-technical spectrum. That is

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.

Other collections of open problems

As with this page, these collections may not be up-to-date.

Itai Benjamini
Krzysztof Burdzy
Tom Liggett
Michel Talagrand