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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Scaling limit of DLA on a long line segment
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by Yingxin Mu, Eviatar B. Procaccia and Yuan Zhang PDF
Trans. Amer. Math. Soc. 375 (2022), 8769-8806 Request permission

Abstract:

In this paper, we prove that the bulk of 2-dimensional DLA starting from a long line segment on the $x$-axis has a scaling limit to the stationary DLA. The main phenomenological difficulty is the multi-scale, non-monotone interaction of the DLA arms. We overcome this via a coupling scheme between the two processes and an intermediate DLA process with absorbing mesoscopic boundary segments. Our result allows to import results from the more amenable infinite stationary DLA process to the more physical finite aggregations.
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Additional Information
  • Yingxin Mu
  • Affiliation: University of Leipzig, Leipzig, Germany
  • MR Author ID: 1400378
  • Email: yingxin.mu@uni-leipzig.de
  • Eviatar B. Procaccia
  • Affiliation: Technion - Israel Institute of Technology
  • MR Author ID: 954587
  • Email: eviatarp@technion.ac.il
  • Yuan Zhang
  • Affiliation: Center for Applied Statistics and School of Statistics, Renmin University of China, Beijing, People’s Republic of China
  • Email: zhang_probab@ruc.edu.cn
  • Received by editor(s): February 26, 2021
  • Received by editor(s) in revised form: April 3, 2022
  • Published electronically: September 28, 2022
  • Additional Notes: Yuan Zhang is the corresponding author
    This research was supported by NSFC Young Scientists Fund (Grant Number 11901012) and National Key R & D Program of China, Project Number 2020YFA0712902
    The authors would like to thank an anonymous fat cat in the Temple of Great Enlightenment (Dajue Si). The manuscript of this paper was first done when YZ was an Assistant Professor at Peking University
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 8769-8806
  • MSC (2020): Primary 60D05, 60G10, 82C24
  • DOI: https://doi.org/10.1090/tran/8771