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Existence and uniqueness of nonsimple multiple SLE

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arxiv 2308.13886 v1 pith:ZLPUVGPV submitted 2023-08-26 math.PR

Existence and uniqueness of nonsimple multiple SLE

classification math.PR
keywords kappamultiplemeasureuniquenessexistencefiniteassociatedassumption
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abstract

We prove the existence and uniqueness of multiple SLE$_\kappa$ associated with any given link pattern for $\kappa\in (4,6]$. We also have the uniqueness for $\kappa\in (6,8)$. The multiple SLE$_\kappa$ law is constructed by first inductively constructing a $\sigma$-finite multiple SLE$_\kappa$ measure and then normalizing the measure whenever it is finite. The total mass of the measure satisfies the conformal covariance, asymptotics and PDE for multiple SLE$_\kappa$ partition functions in the literature subject to the assumption that it is smooth.

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  1. Multiple SLEs for $\kappa\in (0,8)$: Coulomb gas integrals and pure partition functions

    math-ph 2024-06 unverdicted novelty 7.0

    Constructs SLE(κ) partition functions as Coulomb gas integrals for κ∈(0,8), proves positivity and series properties, builds real-analytic pure partition functions, and relates both via meander matrix to define global ...