Stability and chaos in dynamical last passage percolation (Q6593053)

They show that dynamical delocalization holds in the Brownian last passage percolation (Blpp) model: for times \(t\ll n^{1/3}\) the overlap of the ground states is order-\(n\); for times \(t\gg n^{1/3}\) it is \(o(n)\). For each \(k \in [n]\) they let \(B_k\) be an independent Brownian motion, and the energy of an increasing sequence \(0=z_0<z_1<\dots<z_n=n\) is \(\sum_{k=1}^{n} (B_k(z_k)-B_k(z_{k-1}))\). The optimal choice gives the geodesic or ground state of the Blpp. The dynamics is defined by running standard (speed 1) Ornstein-Uhlenbeck processes on each \(B_k\). They study the static properties of the Blpp in their companion paper [\textit{S. Ganguly} and \textit{A. Hammond}, Commun. Am. Math. Soc. 4, 387--479 (2024; Zbl 07901592)]. One key property of this model is an exact version of the Brownian Gibbs property, which is a property originally exposed for the Airy line ensemble. The Blpp is a model that scales to the Airy line ensemble as \(n \to \infty\). After stating their main results they give two heuristic digressions: justifying the scale at which the transition happens by consideration of Bernoulli last passage percolation; and a Fourier decomposition to justify the delocalization transition in terms of earlier work such as [\textit{I. Benjamini} et al., Publ. Math., Inst. Hautes Étud. Sci. 90, 5--43 (1999; Zbl 0986.60002)]. They also summarize an explanation by physicists da Silveira and Bouchaud, although they state this description is imperfect. They cite as highly useful the monograph [\textit{S. Chatterjee}, Superconcentration and related topics. Cham: Springer (2014; Zbl 1288.60001)]. There are useful figures, especially the first figure in the abstract. The article is 90 pages, clearly written.