# Publications

Preprints and submitted papers

Ergodicity of the number of infinite geodesics originating from zero

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.

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