354 research outputs found
Renormalization Group and Probability Theory
The renormalization group has played an important role in the physics of the
second half of the twentieth century both as a conceptual and a calculational
tool. In particular it provided the key ideas for the construction of a
qualitative and quantitative theory of the critical point in phase transitions
and started a new era in statistical mechanics. Probability theory lies at the
foundation of this branch of physics and the renormalization group has an
interesting probabilistic interpretation as it was recognized in the middle
seventies. This paper intends to provide a concise introduction to this aspect
of the theory of phase transitions which clarifies the deep statistical
significance of critical universality
A New Look at the Schouten-Nijenhuis, Fr\"olicher-Nijenhuis and Nijenhuis-Richardson Brackets for Symplectic Spaces
In this paper we re-express the Schouten-Nijenhuis, the Fr\"olicher-Nijenhuis
and the Nijenhuis-Richardson brackets on a symplectic space using the extended
Poisson brackets structure present in the path-integral formulation of
classical mechanics.Comment: 27+1 pages, Latex, no figure
Stochastic Resonance in Two Dimensional Landau Ginzburg Equation
We study the mechanism of stochastic resonance in a two dimensional Landau
Ginzburg equation perturbed by a white noise. We shortly review how to
renormalize the equation in order to avoid ultraviolet divergences. Next we
show that the renormalization amplifies the effect of the small periodic
perturbation in the system. We finally argue that stochastic resonance can be
used to highlight the effect of renormalization in spatially extended system
with a bistable equilibria
Large deviation approach to non equilibrium processes in stochastic lattice gases
We present a review of recent work on the statistical mechanics of non
equilibrium processes based on the analysis of large deviations properties of
microscopic systems. Stochastic lattice gases are non trivial models of such
phenomena and can be studied rigorously providing a source of challenging
mathematical problems. In this way, some principles of wide validity have been
obtained leading to interesting physical consequences.Comment: Extended version of the lectures given by G. Jona-Lasinio at the 9th
Brazilian school of Probability, August 200
Macroscopic current fluctuations in stochastic lattice gases
We study current fluctuations in lattice gases in the macroscopic limit
extending the dynamic approach to density fluctuations developed in previous
articles. More precisely, we derive large deviation estimates for the
space--time fluctuations of the empirical current which include the previous
results. Large time asymptotic estimates for the fluctuations of the time
average of the current, recently established by Bodineau and Derrida, can be
derived in a more general setting. There are models where we have to modify
their estimates and some explicit examples are introduced.Comment: 4 pages, LaTeX, Changed conten
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