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Résumé |
Understanding the geometrical properties of high-dimensional, random energy
landscapes is an important problem in the physics of glassy systems, with plenty
of interdisciplinary applications. Among these properties, an important role is
played by the statistics of stationary points, which is relevant in determining
the evolution of local dynamics within the landscape. In this talk I will focus
on the energy landscape of a simple model for glasses (the so-called spherical
p-spin model) and I will present a framework to compute the statistical
properties of the saddle points surrounding local minima of the landscape. I
will discuss how this computation allows to extract information on the
distribution of energy barriers surrounding the minimum, as well as on its
connectivity in configuration space. I will comment on the dynamical
implications on these results, especially for the activated regime of the
dynamics, relevant when the dimension of configuration space is large but
finite. |
