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By Peter Mörters, Roger Moser, Mathew Penrose, Hartmut Schwetlick, Johannes Zimmer

This ebook is a set of topical survey articles via best researchers within the fields of utilized research and chance idea, engaged on the mathematical description of progress phenomena. specific emphasis is at the interaction of the 2 fields, with articles by means of analysts being obtainable for researchers in likelihood, and vice versa. Mathematical tools mentioned within the booklet contain huge deviation idea, lace growth, harmonic multi-scale ideas and homogenisation of partial differential equations. types according to the physics of person debris are mentioned along versions in keeping with the continuum description of huge collections of debris, and the mathematical theories are used to explain actual phenomena similar to droplet formation, Bose-Einstein condensation, Anderson localization, Ostwald ripening, or the formation of the early universe. the combo of articles from the 2 fields of research and likelihood is extremely strange and makes this e-book an enormous source for researchers operating in all components with reference to the interface of those fields.

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Ferrari, P. A. and Martin, J. B. (2007). Stationary distributions of multi-type totally asymmetric exclusion processes. Ann. Probab. 35(3), 807–32. Ferrari, P. L. (2004). Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues. Comm. Math. Phys. 252(1–3), 77–109. 36 Analysis and stochastics of growth processes and interface models Fulton, W. (1997). Young tableaux, Volume 35 of London Mathematical Society Student Texts. Cambridge University Press: Cambridge. With applications to representation theory and geometry.

Sepp¨ al¨ ainen, T. (1996). A microscopic model for the Burgers equation and longest increasing subsequences. Electron. J. Probab. 1, no. 5, approx. 51 pp. (electronic). Sepp¨ al¨ ainen, T. (1997). Increasing sequences of independent points on the planar lattice. Ann. Appl. Probab. 7(4), 886–98. Sepp¨ al¨ ainen, T. (1998a). Coupling the totally asymmetric simple exclusion process with a moving interface. Markov Process. Related Fields 4(4), 593–628. I Brazilian School in Probability (Rio de Janeiro, 1997).

Rassoul-Agha, F. and Sepp¨ al¨ ainen, T. (2006). The random average process and random walk in a space-time random environment in one dimension. Comm. Math. Phys. 266, 499–545. , Sethuraman, S. and Sepp¨ al¨ainen, T. (2007). Existence of the zero range process and a deposition model with superlinear growth rates. Ann. Probab. 35(4), 1201–49. Bal´ azs, M. and Sepp¨ al¨ ainen, T. (2007a). Exact connections between current fluctuations and the second class particle in a class of deposition models.

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