20 citations · 37 across the 8 of their papers we have counts for
9 papers
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…
Two-sided bounds on free energy of directed polymers on strongly recurrent graphs
Naotaka Kajino, Kosei Konishi, Makoto Nakashima
We study the directed polymers in random environment on an infinite graph on which the underlying random walk satisfies sub-Gaussian heat kernel bounds with spectral dime…
Law of large numbers and fluctuations in the sub-critical and regions for SHE and KPZ equation in dimension
Clément Cosco, Shuta Nakajima, Makoto Nakashima
There have been recently several works studying the regularized stochastic heat equation (SHE) and Kardar-Parisi-Zhang (KPZ) equation in dimension as the smoothing parame…
Free energy of directed polymers in random environment in -dimension at high temperature
Makoto Nakashima
We consider the free energy of the directed polymers in random environment in -dimension. It is known that is of order as . In this paper, we will…
A remark on the bound for the free energy of directed polymers in random environment in 1+2 dimension
Makoto Nakashima
We consider the behavior of the quantity ; the free energy of directed polymers in random environment in dimension, where is inverse temperature. We know that the f…
Nonnegative solutions to stochastic heat equation with nonlinear drift
Makoto Nakashima
We consider one-dimensional stochastic heat equation with nonlinear drift, , where …
Branching random walks in random environment and super-Brownian motion in random environment
Makoto Nakashima
We focus on the existence and characterization of the limit for a certain critical branching random walks in time-space random environment in one dimension which was introduced by…
Super-Brownian motion in random environment as a limit point of critical branching random walks in random environment
Makoto Nakashima
We focus on the existence and its characterization of limit for a certain critical branching random walks in time-space random environment in 1 dimension which was introduced by Bi…
Almost sure central limit theorem for branching random walks in random environment
Makoto Nakashima
We consider the branching random walks in -dimensional integer lattice with time--space i.i.d. offspring distributions. Then the normalization of the total population is a nonne…