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Author Archives: Fabrice Baudoin
Intermittency for the parabolic Anderson model on spaces with sub-Gaussian heat kernel estimates
With Hongyi Chen, Li Chen and Søren Kjærsgaard, we have posted a new paper, Intermittency for the parabolic Anderson model on spaces with sub-Gaussian heat kernel estimates. This is a sequel to our earlier work on bounded domains of recurrent … Continue reading
Riesz transform on eventually Gaussian local trees
With Aobo Chen and Li Chen, we have posted a new paper, Riesz transform on eventually Gaussian local trees which is a companion paper to the paper discussed in the previous post to which we refer for background about Riesz transform … Continue reading
Riesz transforms on the Vicsek set
This post is about a long paper with Aobo Chen and Li Chen, Riesz transforms on the Vicsek set. I want to explain, without too much technicalities, what we prove and put the results into context. As a side note, … Continue reading
Assistant Professor in Probability Theory & Stochastic Analysis
📍 Aarhus University – Department of Mathematics (Ny Munkegade 118, 8000 Aarhus C)🗓 Position start: 1 August 2026 (3-year full-time fixed-term: 1 Aug 2026–31 Jul 2029) Join the vibrant Stochastics Group at the Department of Mathematics, Aarhus University, at the … Continue reading
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Aarhus Summer School in Analysis and Probability
The 6–10 July, 2026, Aarhus Summer School in Analysis and Probability aims to bring together leading experts and young researchers in the areas of analysis, probability theory, and their interactions. The school will feature a series of five hours lecture courses delivered by … Continue reading
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Tagged education, Lectures, mathematics, science, Summer school, writing
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Postdoctoral Positions in Probability Theory and Analysis
Several postdoctoral positions at Aarhus are opening in my group. The earliest possible start date is February 1st 2026, with flexibility for later starts in the spring. These positions are supported by a Villum Investigator Grant and the ERC, offering excellent opportunities … Continue reading
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Lecture notes: A short introduction to Dirichlet spaces
Here are the lecture notes of the minicourse given at NYU Abu Dhabi.
Lecture 7. Further topics
In this lecture let X be a locally compact and complete metric space equipped with a Radon measure μ supported on X. Let (ℰ, ℱ = dom(ℰ)) be a Dirichlet form on X. We assume throughout that the heat semigroup … Continue reading
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Tagged Dirichlet forms, Hunt process, Regular Dirichlet form
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Lecture 6. Gagliardo-Nirenberg inequalities in Dirichlet spaces
Let (X,μ,ℰ,ℱ) be a Dirichlet space and {Pt}t∈[0,∞) denote the associated Markovian semigroup. Throughout the lecture, we shall assume that P_t admits a measurable heat kernel pt(x,y) satisfying, for some C > 0 and β > 0, for μ × … Continue reading
Lecture 5. Examples of Dirichlet spaces
Contents Riemannian manifolds Carnot groups Sierpinski gasket Cheeger space Riemannian manifolds Let (M,g) be an n-dimensional Riemannian manifold with Riemannian volume measure μ and Riemannian distance d. We consider the quadratic form ℰ on M, which is obtained as the … Continue reading
Posted in Dirichlet forms at NYU
Tagged Dirichlet forms, Heat kernel estimates, Sierpinski gasket
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