Shuta Nakajima's Papers

Welcome

Welcome to the collection of research papers by Shuta Nakajima. Here you can find various publications and research works.

Preprints and Submitted Papers

Published or Accepted Papers

  • Equivalence of fluctuations between SHE and KPZ equation in weak disorder regime (with Stefan Junk)
  • Lipschitz-type estimate for the frog model with Bernoulli initial configuration (with Van Hao Can, Naoki Kubota) Mathematical Physics, Analysis and Geometry, 28(1), 2025
  • Asymptotics of the p-capacity in the critical regime to appear in J. Convex Anal (with Cosco Clément, Florian Schweiger)
  • Injectivity of ReLU networks: perspectives from statistical physics (with Antoine Maillard, Afonso S. Bandeira, David Belius, Ivan Dokmanic) Applied and Computational Harmonic Analysis (76)
  • Lipschitz-type estimate for the frog model with Bernoulli initial configuration (joint work with Van Hao Can and Naoki Kubota),
  • Lipschitz continuity of time constants in generalized FPP (with Van Hao Can and Nguyễn Văn Quyết) Stochastic Processes and their Applications
  • Sharp threshold sequence and universality for Ising perception models (with Nike Sun) Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)
  • Fluctuations of two-dimensional stochastic heat equation and KPZ equation in subcritical regime for general initial conditions (with Makoto Nakashima) Electron. J. Probab. 28: 1-38 (2023)
  • Gardner formula for Ising perceptron models at small densities (with Erwin Bolthausen, Nike Sun, Changji Xu) Proceedings of Machine Learning Research vol 178:1–125, 2022
  • A variational formula for large deviations in First-passage percolation under tail estimates (with Clément Cosco) Ann. Appl. Probab. 33(3): 2103-2135
  • Law of large numbers and fluctuations in the sub-critical and $L^2$ regions for SHE and KPZ equation in dimension $d \geq 3$ (with Clément Cosco and Makoto Nakashima) Stochastic Processes and their Applications Volume 151, September 2022, Pages 127-173
  • Maximal edge-traversal time in First Passage Percolation Electron. J. Probab. 27: 1-32 (2022)
  • Triviality of the geometry of mixed p-spin spherical Hamiltonians with external field (with David Belius, Jiří Černý,  Marius Schmidt) Journal of Statistical Physics. volume 186, Article number: 12 (2022)
  • Gaussian fluctuations for the directed polymer partition function for d≥3 and in the whole L2-region (with Cosco Clément) Ann. Inst. H. Poincaré Probab. Statist. 57(2): 872-889 (May 2021)
  • Divergence of non-random fluctuation for Euclidean first-passage percolation Proceeding of "The 12th Mathematical Society of Japan, Seasonal Institute (MSJ-SI) Stochastic Analysis, Random Fields and Integrable Probability.
  • Divergence of non-random fluctuation in First Passage Percolation Electronic Communications in Probability, 2019, Vol. 24, paper no. 65, 1-13.
  • Divergence of shape fluctuation for general distributions in first passage percolation Annales de l’Institut Henri Poincaré - Probabilités et Statistiques Volume 56, Number 2 (2020), 782-791.
  • First passage time of the frog model has a sublinear variance (with Van Hao Can) Electronic Journal of Probability, Online first, 2019.
  • On properties of optimal paths in First-Passage Percolation Journal of Statistical Physics, 174, 259-275, 2019
  • Concentration results for directed polymer with unbounded jumps ALEA, Latin American Journal of Probability and Mathematical Statistics, 15, 1–20 2018
  • Limiting results for the free energy of directed polymers in random environment with unbounded jumps (with Francis Comets, Ryoki Fukushima, Nobuo Yoshida) Journal of Statistical Physics, 161, 577-597, 2015