2015/09/10 by Eliran Subag, Subag, Eliran, Ofer Zeitouni +1 · 3 citations
Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1509.03098
openalex publication_date 2015/09/10 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Recently, sharp results concerning the critical points of the Hamiltonian of\nthe p-spin spherical spin glass model have been obtained by means of moments\ncomputations. In particular, these moments computations allow for the\nevaluation of the leading term of the ground-state, i.e., of the global\nminimum. In this paper, we study the extremal point process of critical points\n- that is, the point process associated to all critical values in the vicinity\nof the ground-state. We show that the latter converges in distribution to a\nPoisson point process of exponential intensity. In particular, we identify the\ncorrect centering of the ground-state and prove the convergence in distribution\nof the centered minimum to a (minus) Gumbel variable. These results are\nidentical to what one obtains for a sequence of i.i.d variables, correctly\nnormalized; namely, we show that the model is in the universality class of REM.\n