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Abstract |
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.
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