153 citations · 463 across the 21 of their papers we have counts for
23 papers
Joint stochastic localization and applications
Tom Alberts, Yiming Xu, Qiang Ye
Stochastic localization is a pathwise analysis technique that has emerged as a powerful tool in high-dimensional probability and sampling. In this work, we extend stochastic locali…
Large deviations of geodesic midpoint fluctuations in last-passage percolation with general i.i.d. weights
Tom Alberts, Riddhipratim Basu, Sean Groathouse +1
The study of transversal fluctuations of the optimal path is a crucial aspect of the Kardar-Parisi-Zhang (KPZ) universality class. In this work, we establish the large deviation li…
Conformal field theory of Gaussian free fields in a multiply connected domain
Tom Alberts, Sung-Soo Byun, Nam-Gyu Kang
We implement a version of conformal field theory (CFT) that gives a connection to SLE in a multiply connected domain. Our approach is based on the Gaussian free field and applies t…
The Green's function of the parabolic Anderson model and the continuum directed polymer
Tom Alberts, Christopher Janjigian, Firas Rassoul-Agha +1
We build a regular version of the field which describes the Green's function, or fundamental solution, of the parabolic Anderson model (PAM) with white noise forcing…
Pole dynamics and an integral of motion for multiple SLE(0)
Tom Alberts, Sung-Soo Byun, Nam-Gyu Kang +1
We describe the Loewner chains of the real locus of a class of real rational functions whose critical points are on the real line. Our main result is that the poles of the rational…
Dimension Results for the Spectral Measure of the Circular Beta Ensembles
Tom Alberts, Raoul Normand
We study the dimension properties of the spectral measure of the Circular -Ensembles. For it it was previously shown by Simon that the spectral measure is almost surel…
On the Geometry of the Last Passage Percolation Problem
Tom Alberts, Eric Cator
We analyze the geometrical structure of the passage times in the last passage percolation model. Viewing the passage time as a piecewise linear function of the weights we determine…
Busemann functions and semi-infinite O'Connell-Yor polymers
Tom Alberts, Firas Rassoul-Agha, Mackenzie Simper
We prove that given any fixed asymptotic velocity, the finite length O'Connell-Yor polymer has an infinite length limit satisfying the law of large numbers with this velocity. By a…
Nested critical points for a directed polymer on a disordered diamond lattice
Tom Alberts, Jeremy Clark
We consider a model for a directed polymer in a random environment defined on a hierarchical diamond lattice in which i.i.d. random variables are attached to the lattice bonds. Our…
Bak-Sneppen Backwards
Tom Alberts, Ga Yeong Lee, Mackenzie Simper
We study the backwards Markov chain for the Bak-Sneppen model of biological evolution and derive its corresponding reversibility equations. We show that, in contrast to the forward…
The intermediate disorder regime for a directed polymer model on a hierarchical lattice
Tom Alberts, Jeremy Clark, Sasa Kocic
We study a directed polymer model defined on a hierarchical diamond lattice, where the lattice is constructed recursively through a recipe depending on a branching number $b\in \ma…
A Dimension Spectrum for SLE Boundary Collisions
Tom Alberts, Ilia Binder, Fredrik Johansson Viklund
We consider chordal SLE(kappa) curves for kappa > 4, where the intersection of the curve with the boundary is a random fractal of almost sure Hausdorff dimension min {2-8/kappa,1}.…
Some partial results on the convergence of loop-erased random walk to SLE(2) in the natural parametrization
Tom Alberts, Michael J. Kozdron, Robert Masson
We outline a strategy for showing convergence of loop-erased random walk on the Z^2 square lattice to SLE(2), in the supremum norm topology that takes the time parametrization of t…
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…
The Intermediate Disorder Regime for Directed Polymers in Dimension 1+1
Tom Alberts, Kostya Khanin, Jeremy Quastel
We introduce a new disorder regime for directed polymers with one space and one time dimension that is accessed by scaling the inverse temperature parameter βwith the length of the…
Bridge Decomposition of Restriction Measures
Tom Alberts, Hugo Duminil-Copin
Motivated by Kesten's bridge decomposition for two-dimensional self-avoiding walks in the upper half plane, we show that the conjectured scaling limit of the half-plane SAW, the SL…
The Covariant Measure of SLE on the Boundary
Tom Alberts, Scott Sheffield
We construct a natural measure mu supported on the intersection of a chordal SLE(kappa) curve gamma with the real line R, in the range 4 < kappa < 8. The measure is a function of t…
Hausdorff dimension of the SLE curve intersected with the real line
Tom Alberts, Scott Sheffield
We establish an upper bound on the asymptotic probability of an SLE(kappa) curve hitting two small intervals on the real line as the interval width goes to zero, for the range 4 <…
Intersection probabilities for a chordal SLE path and a semicircle
Tom Alberts, Michael J. Kozdron
We derive a number of estimates for the probability that a chordal SLE path in the upper half plane H intersects a semicircle centred on the real line. We prove that if 0<kappa<8 a…