Seminars and short courses

In this talk, we will present some recent results concerning the vector-valued mean-field spherical model in a random external field, which is a mean-field generalization of the Berlin-Kac model subject to an additional external random field term in the Hamiltonian. Through the random field term, the Gibbs measures become random Gibbs measures, and their convergence in the infinite volume limit can be studied in different probabilistic modes. For this particular model, we are able to characterize exactly the limit points, convergence in distribution, and convergence in empirical distributions. The properties of the model are closely connected to corresponding limit theorems for random walks, and they exhibit similar dimensional dependence for phenomena like transience and recurrence. Time permitting, we will also discuss the spin glass features of the model. This talk is based on the joint work arXiv:2505.16843 with Professor Christof Külske.