For critical spherical FK–Ising planar maps with n edges, stationary random walks using every incident half-edge converge jointly with the rescaled map metric and degree measure to Liouville Brownian motion on the unit-area √3-quantum sphere when time is accelerated by exactly n; the convergence holds for any fixed finite number of conditionally independent walks.
For critical spherical FK–Ising planar maps with n edges, stationary random walks using every incident half-edge converge jointly with the rescaled map metric and degree measure to Liouville Brownian motion on the unit-area √3-quantum sphere when time is accelerated by exactly n; the convergence holds for any fixed finite number of conditionally independent walks.
For critical spherical FK–Ising planar maps with n edges, stationary random walks using every incident half-edge converge jointly with the rescaled map metric and degree measure to Liouville Brownian motion on the unit-area √3-quantum sphere when time is accelerated by exactly n; the convergence holds for any fixed finite number of conditionally independent walks.
If correct, identifies the intrinsic diffusion and exact deterministic clock for walks on finite critical FK–Ising maps.
Do stationary walks on critical FK–Ising planar maps converge with an exact linear clock to Liouville Brownian motion?
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OpenAI reports Liouville Brownian limits of walks on critical FK–Ising maps
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