Abstract Consider $$(X_{i}(t))$$ ( X i ( t ) ) solving a system of N stochastic differential equations interacting through a random matrix $${\mathbf {J}} = (J_{ij})$$ J = ( J ij ) with independent (not necessarily identically distributed) random coefficients. We show that the trajectories of averaged observables of $$(X_i(t))$$ ( X i ( t ) ) , initialized from some $$\mu $$ μ independent of $${\mathbf {J}}$$ J , are universal, i.e., only depend on the choice of the distribution $$\mathbf {J}$$ J through its first and second moments (assuming e.g., subexponential tails). We take a general combinatorial approach to proving universality for dynamical systems with random coefficients, combining a stochastic Taylor expansion with a moment matchingtype argument. Concrete settings for which our results imply universality include aging in the spherical SK spin glass, and Langevin dynamics and gradient flows for symmetric and asymmetric Hopfield networks.
Finite chemical potential equation of state for QCD from an alternative expansion scheme
The Taylor expansion approach to the equation of state of QCD at finite chemical potential struggles to reach large chemical potential μ B . This is primarily due to the intrinsic diffculty in precisely determining higher order Taylor coefficients, as well as the structure of the temperature dependence of such observables. In these proceedings, we illustrate a novel scheme [1] that allows us to extrapolate the equation of state of QCD without suffering from the poor convergence typical of the Taylor expansion approach. We continuum extrapolate the coefficients of our new expansion scheme and show the thermodynamic observables up to μ B / T ≤ 3.5.
 Editors:
 David, G.; Garg, P.; Kalweit, A.; Mukherjee, S.; Ullrich, T.; Xu, Z.; Yoo, I.K.
 Award ID(s):
 1654219
 Publication Date:
 NSFPAR ID:
 10336539
 Journal Name:
 EPJ Web of Conferences
 Volume:
 259
 Page Range or eLocationID:
 10015
 ISSN:
 2100014X
 Sponsoring Org:
 National Science Foundation
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