Shuta Nakajima

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math.PR2026

On the most likely geodesic in last passage percolation

Sam McKeown, Shuta Nakajima

We consider the problem of identifying the paths most likely to occur as geodesics in last passage percolation. Heuristics suggest that these modal paths should be the extreme corn…

math.PR2026

Sharp behavior of the free energy for the two-dimensional directed polymer model

Quentin Berger, Shuta Nakajima

We consider the directed polymer model on $Z^{d}$ , in an i.i.d.\ random environment $I ¨ = (I ¨ _{n, x})_{n \geq 0, x \in Z^{d}}$ , focusing on the critical dimension $d = 2$ . Our…

math.PR2024

Lipschitz-continuity of time constant in generalized First-passage percolation

Van Hao Can, Shuta Nakajima, Van Quyet Nguyen

In this article, we consider a generalized First-passage percolation model, where each edge in $Z^{d}$ is independently assigned an infinite weight with probability $1 - p$ , a…