Research

Gibbs measures in statistical physics and quantum field theory

1. (with N. Barashkov, P. Sosoe) Sharp phase transition in the grand canonical Φ^3 measure at critical chemical potential 

2. (with P. Sosoe) Central limit theorem for the focusing Φ^4-measure in the infinite volume limit

3. (with P. Sosoe) Large deviations and free energy of Gibbs measure for the dynamical Φ^3-model in infinite volume

4. (with B. Gess, P. Tsatsoulis) Low-temperature expansions for the Euclidean Φ^4_2-measure

5. (with T. Robert, L. Tolomeo, Y. Wang) Focusing Gibbs measures with harmonic potential, Ann. Inst. Henri Poincaré Probab. Stat. 61 (2025), no. 1, 571–598. 

6. (with T. Oh, L. Tolomeo)  A remark on Gibbs measures with log-correlated Gaussian fields, Forum Math. Sigma. 12 (2024), e50, 40 pp.

Transport properties of Gibbs and Gaussian measures under the flow of Hamiltonian PDEs 

1. Phase transition of singular Gibbs measures for three-dimensional Schrödinger-wave system

2. Invariant Gibbs dynamics for the two-dimensional Zakharov-Yukawa system, J. Funct. Anal. 286, (2024), no. 4, 81 pp  

3. (with J. Forlano) Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations, Comm. Partial Differential Equations, 47 (2022), no. 6, 1296--1337. 

4. (with T. Oh) Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation in negative Sobolev spaces, J. Funct. Anal. 281 (2021), no. 9, 49 pp.

Ergodicity, mixing, and SPDEs

1. (with H.D. Nguyen) Polynomial mixing for the stochastic Schrödinger equation with large damping on the whole space

2. Exponential ergodicity for the stochastic hyperbolic sine-Gordon equation on the circle, J. Stat. Phys. 191 (2024), no. 10, Paper No. 124, 31 pp.  

3. (with F. Otto, M. Tempelmayr) Lecture notes on tree-free regularity structures, Mat. Contemp. 58 (2023), 150–196.  

Deterministic PDEs

1. Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation, Commun. Pure Appl. Anal. 19 (2020), no. 12, 5437–5473.  

2. Well-posedness and ill-posedness for the fourth order cubic nonlinear Schrödinger equation in negative Sobolev spaces, J. Math. Anal. Appl. 504 (2021), no. 1, Paper No. 125342, 41 pp.

Other articles

• Oberwolfach report, Quantum field theory and stochastic PDEs: Langevin Dynamics of Lattice Yang-Mills measures 

• HORIZON (webzine issued by KIAS (Korea Institute for Advanced Study): 편미분 방정식을 이용한 양자장 이론의 건설 [1]: 무한 차원 깁스 측도와 확률 편미분방정식

• HORIZON (webzine issued by KIAS (Korea Institute for Advanced Study): 편미분 방정식을 이용한 양자장 이론의 건설 [2]:재규격화와 파인만 다이어그램