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math.PR2024
Improvement of Wu's logarithmic Sobolev inequality via the Poisson-Föllmer process
Shrey Aryan, Pablo López-Rivera, Yair Shenfeld
We give an alternative proof to Wu's logarithmic Sobolev inequality for the Poisson measure on the nonnegative integers using a stochastic variational formula for entropy. We show…
math.AP2024
Soliton resolution for the energy-critical nonlinear heat equation in the radial case
Shrey Aryan
We establish the Soliton Resolution Conjecture for the radial critical non-linear heat equation in dimension Thus, every finite energy solution resolves, continuously in…
math.AP2024
Concavity for elliptic and parabolic equations in locally symmetric spaces with nonnegative curvature
Shrey Aryan, Michael B. Law
We establish a concavity principle for solutions to elliptic and parabolic equations on locally symmetric spaces with nonnegative sectional curvature, extending the results of Lang…