Localization and Perron–Frobenius Theory for Directed Polymers
نویسندگان
چکیده
منابع مشابه
Localization and Perron–frobenius Theory for Directed Polymers
We consider directed polymers in a random potential given by a deterministic profile with a strong maximum at the origin taken with random sign at each integer time. We study two main objects based on paths in this random potential. First, we use the random potential and averaging over paths to define a parabolic model via a random Feynman–Kac evolution operator. We show that for the resulting ...
متن کاملTheory of directed polymers.
We develop a theory of polymers in a nematic solvent by exploiting an analogy with two-dimensional quantum bosons at zero temperature. We argue that the theory should also describe polymers in an isotropic solvent. The dense phase is analyzed in a Bogoliubovlike approximation, which assumes a broken symmetry in the phase of the boson order parameter. We find a stiffening of the longitudinal flu...
متن کاملStrong localization and macroscopic atoms for directed polymers
In this article, we derive strong localization results for directed polymers in random environment. We show that at ”low temperature” the polymer measure is asymptotically concentrated at a few points of macroscopic mass (we call these points ǫ-atoms). These results are derived assuming weak conditions on the tail decay of the random environment. MSC: 60K37;82B44
متن کاملSelf-localization of directed polymers and oppressive population control
We construct a phenomenological theory of self-localization of directed polymers in d+1 dimensions. In d = 1 we show that the polymer is always self-localized, whereas in d = 2 there is a phase transition between localized and free states. We also map this system to a model of population dynamics with fixed total population. Our previous results translate to static and expanding population clus...
متن کاملDirected Polymers in Random Environment: Path Localization and Strong Disorder
We consider directed polymers in random environment. Under mild assumptions on the environment, we prove here: (i) equivalence of decay rate of the partition function with some natural localization properties of the path, (ii) quantitative estimates of the decay of the partition function in dimensions one or two, or at sufficiently low temperature, (iii) existence of quenched free energy. In pa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Moscow Mathematical Journal
سال: 2010
ISSN: 1609-3321,1609-4514
DOI: 10.17323/1609-4514-2010-10-4-667-686