Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp015425k988m
 Title: The One-Dimensional Restriction of the Critical Ising Model under Rescaling and Its Stochastic Integral Authors: Zhang, Xufan Advisors: Sinai, Yakov Contributors: Aizenman, Michael Department: Mathematics Class Year: 2014 Abstract: This paper explores the behavior of the one-dimensional restriction of the critical Ising model under rescaling. In particular, using a “locality” lemma, the rescaled sum PN i=1 σi/N7/8 is proven to converge in distribution. A Monte Carlo experiment is conducted to illustrate what the limiting distribution possibly is. The paper also attempts to construct a stochastic integral based on the model considered above. Finally, the paper provides an exposition of a proof of the “locality” lemma. Extent: 36 pages URI: http://arks.princeton.edu/ark:/88435/dsp015425k988m Type of Material: Princeton University Senior Theses Language: en_US Appears in Collections: Mathematics, 1934-2016

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