The Annals of Probability

Alternating arm exponents for the critical planar Ising model

Hao Wu

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We derive the alternating arm exponents of the critical Ising model. We obtain six different patterns of alternating boundary arm exponents which correspond to the boundary conditions $(\ominus\oplus)$, $(\ominus\operatorname{free})$ and $(\operatorname{free}\operatorname{free})$, and the alternating interior arm exponents.

Article information

Ann. Probab., Volume 46, Number 5 (2018), 2863-2907.

Received: June 2016
Revised: June 2017
First available in Project Euclid: 24 August 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J67: Stochastic (Schramm-)Loewner evolution (SLE)
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Schramm–Loewner evolution critical planar Ising model arm exponent


Wu, Hao. Alternating arm exponents for the critical planar Ising model. Ann. Probab. 46 (2018), no. 5, 2863--2907. doi:10.1214/17-AOP1241.

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