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math.PR2022
On the upper tail large deviation rate function for chemical distance in supercritical percolation
Barbara Dembin, Shuta Nakajima
We consider the supercritical bond percolation on and study the graph distance on the percolation graph called the chemical distance. It is well-known that there exis…
math.PR2022
Sharp threshold sequence and universality for Ising perceptron models
Shuta Nakajima, Nike Sun
We study a family of Ising perceptron models with -valued activation functions. This includes the classical half-space models, as well as some of the symmetric models cons…