论文标题
无序的非释放动力学的平衡浓度和相对不稳定
Concentration of Equilibria and Relative Instability in Disordered Non-Relaxational Dynamics
论文作者
论文摘要
我们考虑了Cugliandolo等人引入的随机自主ods系统。 [22]，它是球形p-spin模型的梯度流的非释放类似物。 Fyodorov [32]在高维限制中计算了该模型中预期均衡数量的渐近数，随后是对Garcia的预期稳定均衡数量的相似计算[38]。我们表明，对于$ p> 9 $，平衡的数量以及稳定的平衡数量集中在各自的平均值上，在放松案例中概括了Subag和Zeitouni [61，64]的最新结果。特别是，我们证实该模型从Ben Acrous，Fyodorov和Khoruzhenko的意义上经历了从相对不稳定性到绝对不稳定性的过渡[11]。
We consider a system of random autonomous ODEs introduced by Cugliandolo et al. [22], which serves as a non-relaxational analog of the gradient flow for the spherical p-spin model. The asymptotics for the expected number of equilibria in this model was recently computed by Fyodorov [32] in the high-dimensional limit, followed a similar computation for the expected number of stable equilibria by Garcia [38]. We show that for $p > 9$ the number of equilibria, as well as the number of stable equilibria, concentrate around their respective averages, generalizing recent results of Subag and Zeitouni [61, 64] in the relaxational case. In particular, we confirm that this model undergoes a transition from relative to absolute instability, in the sense of Ben Arous, Fyodorov, and Khoruzhenko [11].
