Sitemap
A list of all the posts and pages found on the site. For you robots out there, there is an XML version available for digesting as well.
Pages
Posts
Future Blog Post
Published:
This post will show up by default. To disable scheduling of future posts, edit config.yml and set future: false.
Blog Post number 4
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 3
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 2
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 1
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
portfolio
Portfolio item number 1
Short description of portfolio item number 1
Portfolio item number 2
Short description of portfolio item number 2
publications
Asymptotic of the smallest eigenvalues of the continuous Anderson Hamiltonian in (d \leq 3)
Published in Stochastics and Partial Differential Equations: Analysis and Computations, 2022
Recommended citation: Hsu, YS., Labbé, C. Asymptotic of the smallest eigenvalues of the continuous Anderson Hamiltonian in . Stoch PDE: Anal Comp 11, 1089–1122 (2023).
Construction and spectrum of the Anderson Hamiltonian with white noise potential on (\mathbf{R}^2) and (\mathbf{R}^3)
Published in Probability and Mathematical Physics, 2025
Recommended citation: Y.-S. Hsu and C. Labbé, Construction and spectrum of the Anderson Hamiltonian with white noise potential on \(\mathbb{R}^2\) and \(\mathbb{R}^3\), Probab. Math. Phys. 7 (2026), no.~1, 1--35; MR4998450
Landau Hamiltonian with Gaussian white noise potential and the asymptotic of its bottom of spectrum
Published in arXiv, 2025
Recommended citation: Hsu, Yueh-Sheng. "Landau Hamiltonian with Gaussian white noise potential and the asymptotic of its bottom of spectrum." arXiv preprint arXiv:2511.22162 (2025).
Variance renormalisation in regularity structures – the case of (2d) gPAM
Published in arXiv, 2026
Recommended citation: Gerencsér, Máté and Yueh-Sheng Hsu. “Variance renormalisation in regularity structures -- the case of $2d$ gPAM.” (2026).
talks
Variance renormalisation of two dimensional gPAM with differentiated space white noise
Published:
In this work, we consider the gPAM equation with a differentiated space white noise in two dimensions. A particularity of this equation is that it just falls on the borderline of the subcriticality condition; moreover, even if one could have chosen a slightly more regular noise, the variance of certain non-linear functionals of the noise is expected to explode and the local solution theory would still fail. To tame down this variance blowup, a multiplicative renormalisation is introduced. This multiplicative renormalisation was first carried out by [Hairer ‘24] in the case of KPZ, and a general prediction was made there for a wider class of equations. The current work therefore has the objective to show gPAM falls into this picture. It is worth noting that, while a Da Prato-Debussche trick was used in the KPZ case, no such trick is available for gPAM. One thus has to work on the level of singular SPDE machineries such as regularity structure to obtain the desired result.
Sharp convergence rates for singular SPDEs - the case of KPZ
Published:
For subcritical singular SPDEs, the theory of regularity structures typically yields, as the mollification scale \(\varepsilon\to0\), a convergence rate of order \(\varepsilon^\gamma\) for some small \(\gamma>0\). The exponent \(\gamma\) is limited by the gap between the optimal regularity of the driving noise and the regularity in which the noise is measured; in this sense, one can trade regularity of the solution for convergence rate. For instance, under the subcritical and no variance blow-up conditions, in the KPZ equation driven by space-time white noise one obtains \(\gamma<\frac14\), while for \(\Phi^4_3\) one gets \(\gamma<\frac13\). In this work, we show that the optimal exponent for KPZ is \(\gamma=\frac12\). More precisely, we prove if \(u_\varepsilon\) denotes the KPZ solution driven by mollified white noise at scale \(\varepsilon\), then \(\varepsilon^{-1/2}(u_\varepsilon - u_{\varepsilon/2})\) is bounded in \(L^p(\Omega)\) for all \(p \ge 2\) and converges in law to a non-trivial limit \(w\), which solves another singular SPDE driven by an independent white noise. This CLT-type result identifies the optimal convergence rate for KPZ. We also conjecture that the same mechanism yields the optimal rates \(\gamma=1\) for \(\Phi^4_3\) and \(\gamma=2\) for \(\Phi^4_2\), which will be studied in forthcoming work.
teaching
2020-21, 2023-24 - L2 Probability - Tutorial (TD)
Tutorial (TD), Université Paris-Dauphine PSL, CEREMADE, 2023
For the winter semesters of 2020 and 2023, I was responsible for the Bachelor-level tutorial sessions on Probability in Paris-Dauphine University.
2020-2024 - M1 Discrete-time Processes - Tutorial (TD)
Tutorial (TD), Université Paris-Dauphine PSL, CEREMADE, 2024
For four consecutive years (2020 - 2024), I was responsible for the Master-level tutorial sessions on Discrete-time Processes in Paris-Dauphine University, which introduces students to topics such as conditional expectation, martingale theory and Markov chains.
2026 - AKANA AKWTH Stochastic PDEs
Lecture, Technische Unversität Wien, Institut für Analysis und Scientific Computing, 2026
In the summer semester of 2026, I will give a Master-level course on stochastic partial differential equations. The lecture is designed to give an overall introduction to different aspects in modern SPDE theory.