Jian Ding: Repeated emergence of 4/3-exponent

In this talk, I will describe the emergence of the 4/3-exponent in two seemingly unrelated models: random distance of Liouville quantum gravity and correlation length for the two-dimensional random field Ising model. I will then explain that such 4/3-exponent, while being unexpected among respective communities even from a physics perspective, has in fact been hinted in Leighton-Shor (1989) and Talagrand (2014) where the 4/3-exponent emerges in a random matching problem. Finally, I will present the heuristic computation which leads to the emergence of the 4/3-exponent.
While I will review related progress on these topics, the two papers featuring 4/3-exponent are with Subhajit Goswami and with Mateo Wirth.

One world IAMP mathematical physics seminar