Abstract
We explore the behavior under scaling limits of large systems using methods from the theory large deviations. This is carried out through the examination of a few examples.
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Jensen, L.: Large Deviations of the Asymmetric Simple Exclusion Process. NYU. Ph.D. Thesis (2000)
Olla S., Varadhan S.R.S., Yau H.-T.: Hydrodynamical limit for a Hamiltonian system with weak noise. Commun. Math. Phys. 155(3), 523–560 (1993)
Quastel J.: Diffusion of color in the simple exclusion process. Commun. Pure Appl. Math. 45(6), 623–679 (1992)
Quastel J., Rezakhanlou F., Varadhan S.R.S.: Large deviations for the symmetric simple exclusion process in dimensions d ≥ 3. Probab. Theory Relat. Fields 113(1), 1–84 (1999)
Rezakhanlou F.: Propagation of chaos for symmetric simple exclusions. Commun. Pure Appl. Math. 47(7), 943–957 (1994)
Varadhan, S.R.S.: Lectures on hydrodynamic scaling. Hydrodynamic limits and related topics (Toronto, ON, 1998). Fields Inst. Commun., vol. 27, pp. 3–40. Amer. Math. Soc., Providence (2000)
Varadhan, S.R.S.: Large deviations for the asymmetric simple exclusion process. Stochastic analysis on large scale interacting systems. Adv. Stud. Pure Math., vol. 39, pp. 1–27. Math. Soc. Japan, Tokyo (2004)
Ventcel, A.D., Freidlin, M.I.: Small random perturbations of dynamical systems. Uspehi Mat. Nauk 25(1) (151), 3–55 (1970) (Russian)
Vilensky, Y.: Large Deviation Lower Bounds for the Totally Asymmetric Simple Exclusion Process. NYU. Ph.D. Thesis (2008)
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Varadhan, S.R.S. Large Deviations and Scaling Limit. Lett Math Phys 88, 175–185 (2009). https://doi.org/10.1007/s11005-009-0303-x
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DOI: https://doi.org/10.1007/s11005-009-0303-x