Greven A, den Hollander F (1994)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 1994
Publisher: Springer Verlag (Germany)
Book Volume: 100
Pages Range: 301-328
Journal Issue: 3
DOI: 10.1007/BF01193703
This paper solves the second of two variational problems arising in the study of an infinite system of particles that branch and migrate in a random medium. This variational problem involves a non-linear functional on a subset of the stationary probability measures on [ℕ×ℝ], describing the interplay between particles and medium. It is shown that the variational problem can be solved in terms of the Lyapunov exponent of a product of random ℕ×ℕ matrices. This Lyapunov exponent is calculated via a random continued fraction. By analyzing the latter we are able to compute the maximum and the maximizer in the variational problem. It is found that these quantities exhibit interesting non-analyticities and changes of sign as a function of model parameters, which correspond to phase transitions in the infinite particle system. By combining with results from Part I we obtain a complete picture of the phase diagram. © 1994 Springer-Verlag.
APA:
Greven, A., & den Hollander, F. (1994). On a variational problem for an infinite particle system in a random medium Part II: The local growth rate. Probability Theory and Related Fields, 100(3), 301-328. https://dx.doi.org/10.1007/BF01193703
MLA:
Greven, Andreas, and Frank den Hollander. "On a variational problem for an infinite particle system in a random medium Part II: The local growth rate." Probability Theory and Related Fields 100.3 (1994): 301-328.
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