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We prove a lower bound on the size of bottlenecks in uniformquadrangulations, valid at all scales simultaneously. We use it to establishupper bounds on the uniform mixing time of the lazy random walk on uniformquadrangulations, as well as on their dual. The proofs involve an explicitcomputation of the Laplace transform of the number of faces in truncated hullsof the uniform infinite plane quadrangulation.

Uniform mixing time and bottlenecks in uniform finite quadrangulations