The free energy of the random walk pinning model |
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Authors: | Makoto Nakashima |
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Institution: | Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, Japan |
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Abstract: | We consider the random walk pinning model. This is a random walk on whose law is given as the Gibbs measure , where the polymer measure is defined by using the collision local time with another simple symmetric random walk on up to time . Then, at least two definitions of the phase transitions are known, described in terms of the partition function and the free energy. In this paper, we will show that the two critical points coincide and give an explicit formula for the free energy in terms of a variational representation. Also, we will prove that if is smaller than the critical point, then under satisfies the central limit theorem and the invariance principle -almost surely. |
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Keywords: | 60K35 82B26 82B44 Random walk pinning model Free energy Delocalization Localization Central limit theorem Invariance principle |
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