Prob/Stat Seminar

The Prob/Stat Seminar will meet Fridays from 11am to noon in the department seminar room, CU 239.


Mar. 1
Rohan Sarkar (UConn)
Dimension independent functional inequalities by tensorization and projection arguments

We study stability under tensorization and projection-type operations of gradient-type estimates and other functional inequalities for Markov semigroups on metric spaces. With the help of some transportation-type inequalities obtained by Baudoin-Eldredge (EJP, 2021), we prove that the constants in the gradient estimates are independent of the dimension. Our results are applicable to hypoelliptic diffusions on sub-Riemannian manifolds and some hypocoercive diffusions. As a byproduct of our method, we obtain dimension- independent reverse Poincaré, reverse log-Sobolev, and gradient bounds for Lie groups with transverse symmetry and for non-isotropic Heisenberg groups. This is a joint work with Fabrice Baudoin (Arhus University) and Maria Gordina (University of Connecticut).


Mar. 22 (Zoom)
Nages Shanmugalingam (U. Cincinnati)
Using Gromov hyperbolic graphs to approach compact doubling metric measure spaces

Every Cantor set can be realized as the boundary of a tree. In this talk we will describe a way of realizing any compact doubling metric space as the visual boundary of a Gromov hyperbolic graph, and describe a uniformization procedure that gives the compact metric space as the boundary of a uniform domain. This allows us to link Sobolev-type spaces with local energies on uniform domains to Besov spaces with nonlocal energies on the compact metric space.


Apr. 12
Phanuel Mariano (Union College)
Bounds for the Hot Spots Constant

In this talk we discuss the Hot Spots constant for bounded smooth domains that was recently introduced by S. Steinerberger as a means to control the global extrema of the first nontrivial eigenfunction of the Neumann Laplacian by its boundary extrema. We use probabilistic techniques to derive a general formula for a dimension-dependent upper bound that can be tailored to any specific class of bounded Lipschitz domains. This formula is then used to compute upper bounds for the Hot Spots constant of the class of all bounded Lipschitz domains in R^d for both small and asymptotically large d that significantly improve upon the existing results. Moreover, we prove new bounds for the Hot Spots constant for Lipschitz domains on Riemannian manifolds with non-negative Ricci curvature. This is joint work with Hugo Panzo (St. Louis) and Jing Wang (Purdue).


Apr. 19
Pax Kivimae (NYU)
TBA

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Apr. 26 (Zoom)
Jan Beran (U. Konstanz)
TBA

TBA


May 3
Qiang Wu (U. Minnesota)
TBA

TBA


This page is maintained on behalf of the probability and statistics group by Robert Neel; please email robert.neel(at)lehigh.edu with any quesions.