Directed Polymers

On the passage time geometry of the last passage percolation problem
We analyze the geometrical structure of the passage times in the last passage percolation model. Viewing the passage time as a …
Tom Alberts, Eric Cator
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Busemann functions and semi-infinite O'Connell-Yor polymers
We prove that given any fixed asymptotic velocity, the finite length O’Connell-Yor polymer has an infinite length limit …
Tom Alberts, Firas Rassoul-Agha, Mackenzie Simper
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Nested critical points for a directed polymer on a disordered diamond lattice
We consider a model for a directed polymer in a random environment defined on a hierarchical diamond lattice in which i.i.d. random …
Tom Alberts, Jeremy Clark
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The intermediate disorder regime for a directed polymer model on a hierarchical lattice
We study a directed polymer model defined on a hierarchical diamond lattice, where the lattice is constructed recursively through a …
Tom Alberts, Jeremy Clark, Saša Kocić
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The intermediate disorder regime for directed polymers in dimension $1+1$
We introduce a new disorder regime for directed polymers in dimension $1+1$ that sits between the weak and strong disorder regimes. We …
Tom Alberts, Konstantin Khanin, Jeremy Quastel
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Diffusions of multiplicative cascades
A multiplicative cascade can be thought of as a randomization of a measure on the boundary of a tree, constructed from an iid …
Tom Alberts, Ben Rifkind
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The continuum directed random polymer
Motivated by discrete directed polymers in one space and one time dimension, we construct a continuum directed random polymer that is …
Tom Alberts, Konstantin Khanin, Jeremy Quastel
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The near-critical scaling window for directed polymers on disordered trees
We study a directed polymer model in a random environment on infinite binary trees. The model is characterized by a phase transition …
Tom Alberts, Marcel Ortgiese
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