Tail decay for the distribution of the endpoint of a directed polymer

Thomas Bothner, Karl Liechty

We obtain an asymptotic expansion for the tails of the random variable $\tcal=\arg\max_{u\in\mathbb{R}}(\mathcal{A}_2(u)-u^2)$ where ${\mathcal{A}}_2$ is the Airy${}_2$ process. Using…