644 citations · 2.2k across the 41 of their papers we have counts for
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Asymptotics of the -capacity in the critical regime
Clément Cosco, Shuta Nakajima, Florian Schweiger
In this note, we are interested in the asymptotics as of the -capacity between the origin and the set , where is the boundary of the unit ball of the lattic…
Gardner formula for Ising perceptron models at small densities
Erwin Bolthausen, Shuta Nakajima, Nike Sun +1
We consider the Ising perceptron model with N spins and M = N*alpha patterns, with a general activation function U that is bounded above. For U bounded away from zero, or U a one-s…
Triviality of the geometry of mixed -spin spherical Hamiltonians with external field
David Belius, Jiří Černý, Shuta Nakajima +1
We study isotropic Gaussian random fields on the high-dimensional sphere with an added deterministic linear term, also known as mixed p-spin Hamiltonians with external field. We pr…
Fluctuations of two-dimensional stochastic heat equation and KPZ equation in subcritical regime for general initial conditions
Shuta Nakajima, Makoto Nakashima
The solution of Kardar-Parisi-Zhang equation (KPZ equation) is solved formally via Cole-Hopf transformation , where is the solution of multiplicative stochastic heat…
A variational formula for large deviations in First-passage percolation under tail estimates
Clément Cosco, Shuta Nakajima
Consider first passage percolation with identical and independent weight distributions and first passage time . In this paper, we study the upper tail large deviations $\m…