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On the Smoothness of the Partition Function for Multiple Schramm–Loewner Evolutions

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Abstract

We consider the measure on multiple chordal Schramm–Loewner evolution (\(\textit{SLE}_\kappa \)) curves. We establish a derivative estimate and use it to give a direct proof that the partition function is \(C^2\) if \(\kappa < 4\).

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Authors and Affiliations

  1. Department of Statistics, The University of Chicago, 5747 S. Ellis Avenue, Chicago, IL, 60637, USA

    Mohammad Jahangoshahi

  2. Department of Mathematics, The University of Chicago, 5734 University Avenue, Chicago, IL, 60637, USA

    Gregory F. Lawler

Authors
  1. Mohammad Jahangoshahi
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  2. Gregory F. Lawler
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Corresponding author

Correspondence to Mohammad Jahangoshahi.

Additional information

This research supported by National Science Foundation Grant DMS-1513036.

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Jahangoshahi, M., Lawler, G.F. On the Smoothness of the Partition Function for Multiple Schramm–Loewner Evolutions. J Stat Phys 173, 1353–1368 (2018). https://doi.org/10.1007/s10955-018-2165-z

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  • DOI: https://doi.org/10.1007/s10955-018-2165-z

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