We construct a small time strong solution to a nonlocal Hamilton–Jacobi equation (1.1)
introduced in [48], the so-called master equation, originating from the theory of Mean Field …

This manuscript constructs global in time solutions to master equations for potential mean
field games. The study concerns a class of Lagrangians and initial data functions that are …

We study the Bellman equation in the Wasserstein space arising in the study of mean field
control problems, namely stochastic optimal control problems for McKean-Vlasov diffusion …

We propose a conjecture for the limit free energy of mean-field spin glasses with a bipartite
structure, and show that the conjectured limit is an upper bound. The conjectured limit is …

We prove that viscosity solutions of Hamilton--Jacobi--Bellman (HJB) equations,
corresponding either to deterministic optimal control problems for systems of n particles or to …

We establish well-posedness of a class of first order Hamilton–Jacobi equation in geodesic
metric spaces. The result is then applied to solve a Hamilton–Jacobi equation in the …

This paper is a continuation of the program started in [W. Gangbo, S. Mayorga, and A.
Święch, SIAM J. Math. Anal., 53 (2021), pp. 1320–1356]. We consider stochastic optimal …

In this note we prove the uniqueness of solutions to a class of mean field games systems
subject to possibly degenerate individual noise. Our results hold true for arbitrary long time …

We continue the study of viscosity solutions of Hamilton–Jacobi equations in metric spaces
initiated in [37]. We present a more complete account of the theory of metric viscosity …

The Parisi formula is a self-contained description of the infinite-volume limit of the free
energy of mean-field spin glass models. We showthat this quantity can be recast as the …