5 papers
Feynman--Kac formula for the heat equation with a one-center point interaction in
Makoto Nakashima
We study Schrödinger operators with a one-center point interaction, formally defined by \begin{align*} -Î_α=-Î+α\,δ_0(\cdot), \end{align*} for , and the asso…
An upper bound of the lower tail of the mass of balls under the critical stochastic heat flow
Makoto Nakashima
We study the critical two-dimensional stochastic heat flow , recently constructed as the scaling limit of directed polymers in a random environment and a…
Stochastic quantization of the three-dimensional polymer measure via the Dirichlet form method
Sergio Albeverio, Seiichiro Kusuoka, Song Liang +1
We prove that there exists a diffusion process whose invariant measure is the three dimensional polymer measure for all . We follow in part a previous incomplete unpu…
A note on the asymptotics of the free energy of dimensional directed polymers in random environment at high temperature
Makoto Nakashima
The author gave the sharp asymptotic behavior of the free energy of dimensional directed polymers in random environment(DPRE) as the inverse temperature under the a…
Martingale measure associated with the critical stochastic heat flow
Makoto Nakashima
In [CSZ23], the authors proved the convergence of the finite dimensional time distribution of the rescaled random fields derived from the discrete stochastic heat equation of -…