Tom Alberts portrait
  • Associate Professor, Mathematics
801-585-1643

Publications

  • Tom Alberts & Raoul Normand (2022). Dimension Results for the Spectral Measure of the Circular Beta Ensembles. Institute of Mathematical Statistics. Vol. 32, 4642-4680. Published, 12/06/2022.
    https://doi.org/10.1214/22-AAP1798
  • Tom Alberts, Chris Janjigian, Firas Rassoul-Agha & Timo Seppalainen (2022). The Green's function of the parabolic Anderson model and the continuum directed polymer. [Website/Blog] URL https://arxiv.org/abs/2208.11255. Published, 08/01/2022.
    https://arxiv.org/abs/2208.11255
  • Tom Alberts (2021). The Burton-Pemantle Theorem. [Website/Blog] URL http://www.math.utah.edu/~alberts/notes/burton-pemantle/. Published, 12/09/2021.
    http://www.math.utah.edu/~alberts/notes/burton-pem...
  • Tom Alberts & Eric Cator (2021). On the passage time geometry of the last passage percolation problem. ALEA, Lat. Am. J. Probab. Math. Stat. Published, 06/01/2021.
    https://doi.org/10.30757/alea.v18-10
  • Tom Alberts, Nam-Gyu Kang & Nikolai Makarov (2020). Pole Dynamics and an Integral of Motion for Multiple SLE(0). [Website/Blog] URL https://arxiv.org/pdf/2011.05714/. Published, 11/11/2020.
    https://arxiv.org/pdf/2011.05714/
  • The Intermediate Disorder Regime for a Directed Polymer Model on a Hierarchical Diamond Lattice. Alberts T., Clark J., & Kocic S., arXiv:1508.04791 [math.PR] (2015). Published, 10/2017.
    https://doi.org/10.1016/j.spa.2017.02.011
  • Alberts, Tom & Clark, Jeremy (2017). Nested Critical Points for a Directed Polymer on a Disordered Diamond Lattice. Journal of Theoretical Probability. 1-26. Published, 10/2017.
    https://doi.org/10.1007/s10959-017-0787-8
  • Bak-Sneppen Backwards. Alberts, T., Lee G.Y., & Simper M. Stochastics, doi: 10.1080/17442508.2017.1282957 (2017). Published, 01/2017.
    http://www.tandfonline.com/doi/abs/10.1080/1744250...
  • A Dimension Spectrum for SLE Boundary Collisions. Alberts T., Binder I. & Johannsson Viklund F., Comm. Math. Phys., 343, no. 1, 273-298 (2016). Published, 02/2016.
  • Alberts, Tom, Khanin, Konstantin & Quastel, Jeremy (2014). The Continuum Directed Random Polymer. Journal of Statistical Physics. Vol. 154(1-2), 305-326. Published, 01/2014.
  • Alberts, Tom & Rifkind, Ben (2014). Diffusions of multiplicative cascades. Stochastic Process. Appl. 124(2), 1141-1169. Published, 01/2014.
  • Alberts, Tom, Khanin, Konstantin & Quastel, Jeremy (2014). The intermediate disorder regime for directed polymers in dimension 1+1. Annals of Probability. Vol. 42(3), 1212-1256. Published, 01/2014.
  • Alberts T., Kozdron M. & Masson R. (2013). Some Partial Results on the Convergence of Loop-Erased Random Walk to SLE(2) in the Natural Parameterization. Jour. Stat. Phys., 153, 119-141. Published, 01/2013.
  • Alberts, Tom & Ortgiese, Marcel (2013). The near-critical scaling window for directed polymers on disordered trees. Electronic Journal of Probability. Vol. 18(0). Published, 01/2013.
  • Lawler, Gregory F, Kozdron, Michael J & Alberts, Tom (2012). The Green function for the radial Schramm–Loewner evolution. J. Phys. A: Math. Theor., Vol. 45(49), 494015. Published, 01/2012.
  • Alberts, Tom & Sheffield, Scott (2011). The covariant measure of SLE on the boundary. Prob. Theor. Rel. Fields, Vol. 149(3-4), 331-371. Published, 01/2011.
  • Alberts, Tom, Quastel, Jeremy & Khanin, Kostya (2010). Intermediate Disorder Regime for Directed Polymers in Dimension 1+1. Phys. Rev. Lett., Vol. 105(9). Published, 01/2010.
  • Alberts, Tom & Duminil-Copin, Hugo (2010). Bridge Decomposition of Restriction Measures. Jour. Stat. Phys., Vol. 140(3), 467-493. Published, 01/2010.
  • Kozdron, Michael J & Alberts, Tom (2008). Intersection probabilities for a chordal SLE path and a semicircle. Electron. Comm. Prob., Vol. 13(0). Published, 01/2008.
  • Alberts, Tom & Sheffield, Scott (2008). Hausdorff Dimension of the SLE Curve Intersected with the Real Line. Electron. Jour. Prob., Vol. 13(0). Published, 01/2008.
  • Alberts, T. & Karunamuni, R.J. (2006). A locally adaptive transformation method of boundary correction in kernel density estimation. Journal of Statistical Planning and Inference, Vol. 136(9), 2936-2960. Published, 01/2006.
  • Karunamuni, R.J. & Alberts, T. (2005). On boundary correction in kernel density estimation. Statistical Methodology, Vol. 2(3), 191-212. Published, 01/2005.
  • Karunamuni, Rohana J. & Alberts, Tom (2005). A generalized reflection method of boundary correction in kernel density estimation. Canadian Journal of Statistics, Vol. 33(4), 497-509. Published, 01/2005.
  • Alberts T. & Karunamuni R.J. (2003). A Semiparametric Method of Boundary Correction for Kernel Density Estimation. Statistics and Probability Letters, 61, 287-298. Published, 01/2003.
  • Aggarwala R., Alberts T., Bose C. et al (2001). An Automated Algorithm for Decline Analysis. Proceedings of the Fifth PIMS Industrial Problem Solving Workshop. Published, 06/2001.

Research Statement

Within probability theory and statistical mechanics my research focuses on the Schramm-Loewner Evolution and its relation to discrete lattice models, the Gaussian Free Field, and other two-dimensional conformally invariant systems. Recently I also have interests in directed polymer models and last passage percolation, along with their relation to random walk in random environment.

Research Keywords

  • Statistical Mechanics
  • Probability
  • Convex Geometry

Presentations

Grants, Contracts & Research Gifts

  • Random Matrix Theory for Homogenization of Composites. PI: Kenneth Golden. Co-PI(s): Thomas Alberts, Elena Cherkaev. National Science Foundation, 08/15/2017 - 07/31/2020. Total project budget to date: $353,794.00
  • Conference Proposal: Frontier Probability Days Conference. PI: Thomas Alberts. Co-PI(s): Sunder Sethuraman, Edward Waymire, Firas Rassoul-Agha, Davar Khoshnevisan. National Science Foundation, 06/01/2016 - 05/31/2017. Total project budget to date: $25,000.00
  • Conference Proposal: Conference Grant Application for Thematic Programme on Random Geometry (1502404). PI: Thomas K Alberts. National Science Foundation, 2015 - 12/31/2015. Total project budget to date: $35,000.00
  • Conference Proposal: Frontier Probability Days 2014 (1407136). PI: Sunder Sethuraman. Co-PI(s): Thomas Kelly Alberts. National Science Foundation, 2014 - 02/28/2015. Total project budget to date: $20,000.00
  • STATISTICAL MECHANICS. PI: ALBERTS,THOMAS KELLY. SIMONS FOUNDATION, 09/01/2016 - 08/31/2021. Total project budget to date: $35,000.00
  • CONVEX GEOMETRY. PI: ALBERTS,THOMAS KELLY. UNIVERSITY OF UTAH RESEARCH FO, 01/01/2016 - 06/30/2017. Total project budget to date: $34,922.00