English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Given a simply connected planar domain D, distinct points x,y \in \partial D,and \kappa >0, the Schramm-Loewner evolution SLE_\kappa is a random continuousnon-self-crossing path in the closure of D from x to y. TheSLE_\kappa(\rho_1;\rho_2) processes, defined for \rho_1, \rho_2 > -2, are insome sense the most natural generalizations of SLE_\kappa.  When \kappa \leq 4, we prove that the law of the time-reversal of an\SLE_\kappa(\rho_1;\rho_2) from x to y is, up to parameterization, anSLE_\kappa(\rho_2;\rho_1) from y to x. This assumes that the "force points"used to define SLE_\kappa(\rho_1;\rho_2) are immediately to the left and rightof the SLE seed. A generalization to arbitrary (and arbitrarily many) forcepoints applies whenever the path does not (or is conditioned not to) hit theboundary of D except at the endpoints.  The time-reversal symmetry has a particularly natural interpretation when thepaths are coupled with the Gaussian free field and viewed as rays of a randomgeometry. It allows us to couple two instances of the Gaussian free field (withdifferent boundary conditions) so that their difference is almost surelyconstant on either side of the path. In a fairly general sense, addingappropriate constants to the two sides of a ray reverses its orientation.

Imaginary geometry II: reversibility of SLE_\kappa(\rho_1;\rho_2) for \kappa \in (0,4)