Preprints and submitted papers

Ergodicity of the number of infinite geodesics originating from zero

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 Cle’ment Cosco and Makoto Nakashima)

 A variational formula for large deviations in First-passage percolation under tail estimates. (with Cle’ment Cosco)

Fluctuations of two-dimensional stochastic heat equation and KPZ equation in subcritical regime for general initial conditions (with Makoto Nakashima)

Gardner formula for Ising perceptron models at small densities (with Erwin Bolthausen, Nike Sun, Changji Xu)

Asymptotics of the p-capacity in the critical regime (with Cosco Clément, Florian Schweiger)

Sharp threshold sequence and universality for Ising perception models (with Nike Sun)

Published or accepted papers

Francis Comets, Ryoki Fukushima, Shuta Nakajima, Nobuo Yoshida. Limiting results for the free energy of directed polymers in random environment with unbounded jumps, Journal of Statistical Physics, 161, 577-597, 2015

Shuta Nakajima. Concentration results for directed polymer with unbounded jumps, ALEA, Latin American Journal of Probability and Mathematical Statistics, 15, 1–20 2018 3

Shuta Nakajima. On properties of optimal paths in First-Passage Percolation. Journal of Statistical Physics, 174, 259-275, 2019 1

Van Hao Can, Shuta Nakajima. First passage time of the frog model has a sublinear variance. Electronic Journal of Probability, Online first, 2019.

Shuta Nakajima. Divergence of shape fluctuation for general distributions in first passage percolation. Annales de l’Institut Henri Poincare’ – Probabilite’s et Statistiques Volume 56, Number 2 (2020), 782-791.

Shuta Nakajima. Divergence of non-random fluctuation in First Passage Percolation. Electronic Communications in Probability, 2019, Vol. 24, paper no. 65, 1-13.

Shuta Nakajima. Divergence of non-random fluctuation for Euclidean first-passage percolation. To appear in Proceeding of “The 12th Mathematical Society of Japan, Seasonal Institute (MSJ-SI) Stochastic Analysis, Random Fields and Integrable Probability.

Gaussian fluctuations for the directed polymer partition function for d≥3 and in the whole L2-region (with Cosco Clément) To appear in Annales de l’Institut Henri Poincare’ – Probabilite’s et Statistiques

Triviality of the geometry of mixed p-spin spherical Hamiltonians with external field (with David BeliusJiří Černý, Marius Schmidt) Journal of Statistical Physics. volume 186, Article number: 12 (2022)

Maximal edge-traversal time in First Passage Percolation To appear in Electron. J. Probab.