Tom Alberts

Associate Professor

University of Utah

Department of Mathematics

Contact Information

Research

My main focus of research is in probability theory, and within that I mostly study two-dimensional conformally invariant systems. The basic model of these are the Schramm-Loewner Evolution and its variants. I also have interests in statistical mechanics, random walks in random environments, directed polymer models, last passage percolation, and random matrix theory.

Publications

• Dimension Results for the Spectral Measure of the Circular Beta Ensembles.
  Alberts T. & Normand R., arXiv:1912.07788 [math.PR]. (2019).

• Busemann Functions and Semi-Infinite O'Connell-Yor Polymers.
  Alberts T. & Rassoul-Agha F. & Simper M., Bernoulli, 26, no. 3, 1927-1955. (2019). Online Journal.

• On the Geometry of the Last Passage Percolation Problem.
  Alberts T. & Cator E., arXiv:1907.00407 [math.PR]. (2019).

• Nested Critical Points for a Directed Polymer on a Disordered Diamond Lattice.
  Alberts T. & Clark J., Journal of Theoretical Probability, 32, no. 1, 64-89. (2019). Online Journal.

• Bak-Sneppen Backwards.
  Alberts T. & Lee G.-Y. & Simper M., Stochastics, 89, no. 8, 1127-1142. (2017). Online Journal.

• The Intermediate Disorder Regime for a Directed Polymer Model on a Hierarchical Lattice.
  Alberts T. & Clark J. & Kocic S., Stochastic Processes and their Applications, 127, no. 10, 3291-3330. (2017). Online Journal.

• A Dimension Spectrum for SLE Boundary Collisions.
  Alberts T. & Binder I. & Johansson Viklund F., Communications in Mathematical Physics, 343, no. 1, 273-298. (2016). Online Journal.

• Diffusions of Multiplicative Cascades.
  Alberts T. & Rifkind B., Stochastic Processes and their Applications, 124, no. 2, 1141-1169. (2014). Online Journal.

• Intermediate Disorder for 1+1 Dimensional Directed Polymers.
  Alberts T. & Khanin K. & Quastel J., Annals of Probability, 42, no. 3, 1212-1256. (2014). Online Journal.

• The Continuum Directed Random Polymer.
  Alberts T. & Khanin K. & Quastel J., J. Stat. Phys., 154, no. 1-2, 305-326. (2014). Online Journal.

• Some Partial Results on the Convergence of Loop-Erased Random Walk to SLE(2) in the Natural Time Parameterization.
  Alberts T. & Kozdron M. & Masson R., J. Stat. Phys., 153, no. 1, 119-141. (2013). Online Journal.

• The Near-Critical Scaling Window for Directed Polymers on Disordered Trees.
  Alberts T. & Ortgiese M., Electronic Journal of Probability, 18, no. 19, 24 pp. (2013). Online Journal.

• The Green's function for the radial Schramm-Loewner Evolution.
  Alberts T. & Kozdron M. & Lawler G., J. Phys. A, 45, 494015, 17 pp. (2012). Online Journal.

• The Covariant Measure of SLE on the Boundary.
  Alberts T. & Sheffield S., Probability Theory and Related Fields, 3-4, 331-371. (2011). Online Journal.

• The Intermediate Disorder Regime for Directed Polymers in Dimension 1+1.
  Alberts T. & Khanin K. & Quastel J., Physical Review Letters, 105, 090603. (2010). Online Journal.

• Bridge Decomposition of Restriction Measures.
  Alberts T. & Duminil-Copin H., Journal of Statistical Physics, 140, 3, 467-493. (2010). Online Journal.

• Hausdorff Dimension of the SLE Curve Intersected with the Real Line.
  Alberts T. & Sheffield S., Electronic Journal of Probability, 40, 1166-1188. (2008). Online Journal

• Intersection Probabilities for a Chordal SLE Path and a Semicircle..
  Alberts T. & Kozdron M., Electronic Communications in Probability. 13, 448-460. (2008). Online Journal

• A Locally Adaptive Transformation Method of Boundary Correction in Kernel Density Estimation.
  Karunamuni R.J. & Alberts T., Journal of Statistical Planning and Inference 136, 2936-2960. (2006). Online Journal

• A Generalized Reflection Method of Boundary Correction in Kernel Density Estimation.
  Karunamuni R.J. & Alberts T., Canadian Journal of Statistics, 33, 497-509. (2005). Online Journal.

• On Boundary Correction in Kernel Density Estimation.
  Karunamuni R.J. & Alberts T., Statistical Methodology, 2, 191-212. (2005). Online Journal

• A Semiparametric Method of Boundary Correction for Kernel Density Estimation.
  Alberts T. & Karunamuni R.J., Statistics and Probability Letters, 61, 287-298. (2003). Online Journal

Slide Presentations

• The Intermediate Disorder Regime for Directed Polymers in Dimension 1+1
• Dimension and Measure of SLE on the Boundary
• Bridge Decomposition of Restriction Measures
• An Introduction to the Schramm-Loewner Evolution
• Boundary Correction Methods in Kernel Density Estimation

Teaching

University of Utah

• Statistical Inference I, Fall 2020
• Multilinear Models, Spring 2020
• Mathematical Probability, Fall 2019
• Statistical Inference II, Spring 2019
• Time Series Analysis, Spring 2019
• Statistical Inference I, Fall 2018
• Time Series Analysis, Spring 2018
• Multilinear Models, Spring 2018
• Linear Models I, Fall 2017
• Statistical Inference I, Fall 2016
• Algebraic Combinatorics, Fall 2016
• Applied Statistics I, Fall 2015
• Statistical Inference I, Fall 2015
• Actuarial Mathematics, Spring 2015
• Introduction to Probability, Fall 2014

Caltech

• Introduction to Unitary Group Representations, Winter 2014
• Probability I, Fall 2013
• Statistics, Winter 2013
• Stochastic Analysis, Fall 2012
• Probability II, Winter 2012
• Probability I, Fall 2011

University of Toronto

• Introduction to Stochastic Processes, Spring 2011
• Partial Differential Equations, Fall 2010
• Introduction to Mathematical Finance, Fall 2009
• Introduction to Stochastic Processes, Spring 2009

New York University

• Financial Econometrics and Statistical Arbitrage, Fall 2007
• Interest Rate and Credit Models, Summer 2007
• Interest Rate and Credit Models, Spring 2007
• Financial Econometrics and Statistical Arbitrage, Fall 2006
• Calculus II, Summer 2006
• Risk Management, Spring 2006
• Computing in Finance, Fall 2005
• Calculus I, Summer 2005
• Stochastic Calculus, Spring 2005
• Computing in Finance, Fall 2004
• Business Calculus, Summer 2004
• Business Calculus, Spring 2004