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Research Work

My research lies in the field of Probability Theory and its applications to models of statistical physics (random media, random polymers, Kardar-Parisi-Zhang universality, scaling limits of disordered systems, Stochastic PDEs). I am also interested in the relations to random matrices, PDEs, representation theory and combinatorics.

Lecture Notes & Surveys
Publications
  • Edwards-Wilkinson fluctuations for the directed polymer in the full L^2-regime for dimensions d\geq 3, (with D. Lygkonis), arxiv.2005.12706
  • The geometric Burge correspondence and the partition function of polymer replica, (with E. Bisi and N. O'Connell), arXiv.2001.09145
  • Transition between characters of classical groups, decomposition of Gelfand-Tsetlin patterns and last passage percolation, (with E. Bisi), arxiv.1905.09756
  • The two dimensional KPZ equation in the entire subcritical regime, (with F. Caravenna and R. Sun), to appear Ann. Prob., Vol. 48, No 3, 1086-1127 (2020), arxiv.1812.03911.pdf
  • On the moments of the (2+1)-dimensional directed polymer and stochastic heat equation in the critical window, (with F. Caravenna and R. Sun), Comm. Math. Phys. 372, 1-56 (2019) arxiv.1808.03586
  • The Dickman subordinator, renewal theorems and disordered systems, (with F. Caravenna and R. Sun), Elect. J. Prob., vol 24, no 101, 1-40, (2019), arXiv:1805.01465
  • GOE and {\rm Airy}_{2\to1} marginal distribution via symplectic Schur functions, (with E. Bisi), arXiv:1711.05120, in Probability and Analysis in Interacting Physical Systems, Springer Volume for Raghu Varadhan's 75th birthday
  • Point-to-line polymers and orthogonal Whittaker functions, (with E. Bisi), arXiv:1703.07337, Transactions of the AMS, 371 (2019), 8339-8379
  • Universality in marginally relevant disordered systems, (with F. Caravenna and R. Sun), arxiv:1510.06287, Ann. Appl. Prob. 2017, Vol. 27, No. 5, 3050-3112
  • Variants of geometric RSK, geometric PNG and the multipoint distribution of the log-gamma polymer, (with Vu Lan Nguyen) arXiv:1509.03515, Int. Math. Res. Notices, 2017 (15): 4732-4795
  • High temperature limits of (1+1)-dimensional directed polymer with heavy-tailed disorder, (with P. Dey) arxiv:1503.01054, Ann. Prob., 2016, Vol. 44, No. 6, 4006-4048
  • The continuum disordered pinning model (with F. Caravenna and R. Sun), arXiv:1406.5088, Prob. Theory Rel. Fields, (2016), no. 1-2, 17-59
  • Polynomial chaos and scaling limits of disordered systems (with F. Caravenna and R. Sun, J. Eur. Math. Soc. 19 (2017), 1-65 arXiv: 1312.3357.pdf
  • The Critical Curve of the Random Pinning and Copolymer Models at Weak Coupling (with Q. Berger, F. Caravenna, J. Poisat and R. Sun), Comm. Math. Phys., Volume 326, Issue 2, (2014), 507-530 arXiv:1301.5308
  • Geometric RSK correspondence, Whittaker functions and symmetrized random polymers (with N. O'Connell and T. Seppalainen), Inventiones Math., Volume 197, Issue 2, 361-416 (2014) publisher open access, arxiv:1210.5126
  • Path properties of the disordered pinning polymer in the delocalized regime (with K. Alexander), Ann. Appl. Prob., Vol. 24, No. 2, 599–615 (2014) arXiv:1210.1862

  • Subgaussian concentration and rates of convergence in directed polymers (with K. Alexander) Electronic J. Prob., 18 (2013), no. 5, 1–28. arxiv.1204.1819

  • Tropical combinatorics and Whittaker functions, (with I. Corwin, N. O'Connell, T.Seppalainen), Duke Math J., (2014) Volume 163, Number 3, 513-563 arXiv:1110.3489

  • Strong disorder in semidirected random polymers, Ann. Inst. Henri Poincare (B) Prob. Stat. (2013), Vol. 49, No. 3, 753–780 http://arxiv.org/abs/1009.2693

Proceedings
  • Semidirected random polymers: Strong disorder and localization, Actes des rencontres du CIRM, 2 no. 1, (2010) p. 47-48, journal link
  • Phase transitions in random pinning polymers, Oberwolfach reports, No. 38/2009, 378-379
PhD Thesis