糖心TV

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

• From disordered systems to the Critical 2d Stochastic Heat Flow, (with F. Caravenna and R. Sun), Proceedings of ICM 2026,
• The Critical 2d Stochastic Heat Flow and Related Models, (with F. Caravenna and R. Sun), CIME Lectures Notes,
• , a review paper written in the memory of , Stoch. Proc. and Applications, to appear,
• Discrete Stochastic Analysis notes from a course given at 糖心TV and Academia Sinica and National Centre for Theoretical Sciences, Taipei.
• The 2d KPZ as a marginally relevant disordered system, notes from a mini course given at the
• Some algebraic aspects in KPZ universality, Probability Surveys 19: 590-700 (2022)  
• Sacling limits of disordered systems and disorder relevance (with F. Caravenna, R. Sun), Proceedings of the XVIII International Congress of Mathematical Physics,

Publications

• Singularity and regularity of the critical 2D Stochastic Heat Flow, (with F. Caravenna and R. Sun),
• On the moments of the mass of shrinking balls under the Critical 2d Stochastic Heat Flow, (with Ziyang Liu), Comm. Math. Phys.,
• The Allen-Cahn equation with weakly critical random initial datum, (with S. Gabriel and T. Rosati), Prob. Th. Rel. Fields, 1-74 (2024),
• Non-intersecting path constructions for TASEP with inhomogeneous rates and the KPZ fixed point, (with E. Bisi, Y. Liao, A. Saenz), Comm. Math. Phys., 402, 285–333 (2023),
• The critical 2d Stochastic Heat Flow is not a Gaussian Multiplicative Chaos, (with F. Caravenna and R. Sun), Ann. Prob., 51 (6), 2265-2300 (2023),
• A multivariate extension of the Erdos-Taylor theorem, (with D. Lygkonis), Prob. Th. Rel. Fields, Vol. 189,179–227, (2024),
• Moments of the 2d directed polymer in the subcritical regime and a generalisation of the Erd枚s-Taylor theorem, (with D. Lygkonis), Comm. Math. Phys., 401, 2483–2520 (2023),  
• The critical 2d stochastic heat flow, (with F. Caravenna and R. Sun), Inventiones Math., 233, 325–460 (2023),
• Edwards-Wilkinson fluctuations for the directed polymer in the full L^2-regime for dimensions $d\geq 3$, (with D. Lygkonis), Ann. Inst. Henri Poincar茅 (B) Prob. Stat., 58 (1): 65-104, (2022)
• The geometric Burge correspondence and the partition function of polymer replica, (with E. Bisi and N. O'Connell), Selecta Math. 27, Article number: 100 (2021),
• Transition between characters of classical groups, decomposition of Gelfand-Tsetlin patterns and last passage percolation, (with E. Bisi), Advances Math., Vol 404, B, (2022)
• The two dimensional KPZ equation in the entire subcritical regime, (with F. Caravenna and R. Sun), Ann. Prob., Vol. 48, No 3, 1086-1127 (2020),
• 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)
• The Dickman subordinator, renewal theorems and disordered systems, (with F. Caravenna and R. Sun), Elect. J. Prob., vol 24, no 101, 1-40, (2019),
• GOE and marginal distribution via symplectic Schur functions, (with E. Bisi), , in Springer Volume for Raghu Varadhan's 75th birthday
• Point-to-line polymers and orthogonal Whittaker functions, (with E. Bisi), , Transactions of the AMS, 371 (2019), 8339-8379

• Universality in marginally relevant disordered systems, (with F. Caravenna and R. Sun), , 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) , Int. Math. Res. Notices, 2017 (15): 4732-4795

• High temperature limits of (1+1)-dimensional directed polymer with heavy-tailed disorder, (with P. Dey) , Ann. Prob., 2016, Vol. 44, No. 6, 4006-4048
• The continuum disordered pinning model (with F. Caravenna and R. Sun), , 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
• 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

• 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) ,

• Path properties of the disordered pinning polymer in the delocalized regime (with K. Alexander), Ann. Appl. Prob., Vol. 24, No. 2, 599–615 (2014)

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

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

• Strong disorder in semidirected random polymers, Ann. Inst. Henri Poincare (B) Prob. Stat. (2013), Vol. 49, No. 3, 753–780

• Behavior of the solution of a random semilinear equation, (with S.R.S. Varadhan) Comm. Pure and Appl. Math. 1298--1329.

• Exponential convergence for a periodically driven semilinear heat equation, Ann. Inst. Henri Poinc. - Anal. Non Lineaire , 271-284, AN 26 (2009)

• Lyapounov norms for random walks in low disorder and dimension greater than three, Prob. Theory Rel. Fields Volume 143, Numbers 3-4, (2009)

• Quenched and annealed critical points in polymer pinning models, ( with Ken Alexander) Comm. Math. Phys. 291, 659-689 (2009)

• Equality of Critical Points for Polymer Depinning Transitions with Loop Exponent One, (with Ken Alexander), Ann. Appl. Prob, Volume 20, Number 1 (2010), 356-366

Proceedings

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

PhD Thesis

• Limit theorems for a periodically or randomly driven semilinear equation (supervised by S.R.S. Varadhan)