Ημερομηνία: Πέμπτη 5/3/2026

Ώρα: 13:00 - 14:00

Αίθουσα: Γ31

Ομιλητής: Έφη Παπαγεωργίου, Institut für Mathematik, Universität Paderborn. (https://sites.google.com/view/effiepapageorgiou/home)

Title: l^p asymptotic behavior of isotropic transition densities on homogeneous trees

Abstract: We study the large-time l^p behavior of transition densities of an isotropic ran- dom walk in homogeneous trees, which are infinite, connected, acyclic graphs in which every vertex has the same degree, and can be thought as discrete counter- parts of hyperbolic space. Caloric functions of interest are then convolutions of these transition densities
with a finitely supported initial condition, and we are interested in their large time behavior in l^p norm.

For each p ∈ [1, ∞], we introduce a notion of a p-mass function and prove that caloric functions with compactly supported initial data, asymptotically decouple as the product of this mass function the transition density. Using tools of Fourier analysis available on such graphs, we show that this function even boils down to a constant, still depending on p, if the initial condition is radial, that is, depends only on the distance to the origin. Determining the spatial concentration of the densities in p-norm plays an important role, in turn clarifying the
interplay between the exponential volume growth of the graph and heat diffusion. The results extend to affine buildings, even exotic ones beyond the Bruhat–Tits framework.

Joint work with B. Trojan.

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Ιστοσελίδα σεμιναρίου: https://sites.google.com/view/nkua-math-colloquium/