153 citations · 463 across the 21 of their papers we have counts for
5 papers · 1 filter
The Green's function for the radial Schramm-Loewner evolution
Tom Alberts, Michael J. Kozdron, Gregory F. Lawler
We prove the existence of the Green's function for radial SLE(k) for k<8. Unlike the chordal case where an explicit formula for the Green's function is known for all values of k<8,…
The near-critical scaling window for directed polymers on disordered trees
Tom Alberts, Marcel Ortgiese
We study a directed polymer model in a random environment on infinite binary trees. The model is characterized by a phase transition depending on the inverse temperature. We concen…
Diffusions of Multiplicative Cascades
Tom Alberts, Ben Rifkind
A multiplicative cascade can be thought of as a randomization of a measure on the boundary of a tree, constructed from an iid collection of random variables attached to the tree ve…
The Continuum Directed Random Polymer
Tom Alberts, Konstantin Khanin, Jeremy Quastel
Motivated by discrete directed polymers in one space and one time dimension, we construct a continuum directed random polymer that is modeled by a continuous path interacting with…
The intermediate disorder regime for directed polymers in dimension
Tom Alberts, Konstantin Khanin, Jeremy Quastel
We introduce a new disorder regime for directed polymers in dimension that sits between the weak and strong disorder regimes. We call it the intermediate disorder regime. It…