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Onsager Machlup functional for $ ext{SLE}_κ$ loop measures | | Marco Carfagnini
; Yilin Wang
; | | Date: |
1 Nov 2023 | | Abstract: | We relate two ways to renormalize the Brownian loop measure on the Riemann sphere. One by considering Brownian loop measure on the sphere minus a small disk which is known as the normalized Brownian loop measure; the other one by taking the measure on simple loops induced by the outer boundary of the Brownian loops, known as Werner's measure. This result allows us to interpret the Loewner energy as an Onsager--Machlup functional for SLE$_kappa$ loop measure for any fixed $kappa in (0, 4]$, and more generally, for any Malliavin--Kontsevich--Suhov loop measure of the same central charge. | | Source: | arXiv, 2311.00209 | | Services: | Forum | Review | PDF | Favorites | |
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