Claudia C. Raithel

Personal Homepage

Welcome to my webpage!  I am an applied analyst working at the intersection of partial differential equations and stochastics. Currently, I am a postdoc at the TU Wien, where I hold an Austrian Science Fund (FWF) ESPRIT fellowship hosted by the group of Prof. Elisa Davoli. As PI, I lead the ESPRIT project “Effective Large-Scale Models for Random Diffusive Systems”. Previously, I was a postdoc at the TU Dresden in the group of Prof. Stefan Neukamm and also at the TU Wien in the group of Prof. Ansgar Jüngel. I completed my PhD in 2019 under the supervision of Prof. Felix Otto at the Max Planck Institute for Mathematics in the Sciences in Leipzig. My main research interests are quantitative stochastic homogenization of elliptic and parabolic PDEs (in particular, boundary phenomena or situations in which the material sample has macroscopic defects such as cracks, edges, or corners); stochastic particle systems (in particular, fluctuating hydrodynamics models); and cross-diffusion models such as the Maxwell–Stefan model for non-Fickian diffusion.

Contact Details

Research Areas

Stochastic homogenization of linear elliptic PDEs:  The central qualitative result in the homogenization of linear elliptic PDEs is classical and states that, under the assumptions of stationarity and ergodicity, as one zooms out, a linear elliptic PDE with random coefficients may be approximated (in some sense, almost surely) by a homogenized PDE with constant coefficients. In recent years robust theories have been developed that yield quantitative results describing the homogenization process under various quantifications of the ergodicity assumption. In my research, I have mainly been interested in settings in which the classical stationarity assumption is broken (e.g., when there is a boundary or an interface) or when the macroscopic situation is itself in some sense singular (e.g., in domains with corners, edges, or cracks).
[1], [2], [4], [7], [8], [10]

Interacting particle systems:  I am mainly interested in McKean–Vlasov diffusion systems, where the “microscopic” description is given by a system of SDEs for the individual particle positions. These are, in particular, mean-field systems, meaning that the total interaction of a particle with all the others may be described in an “averaged” way. Due to the computational cost of simulating many-particle systems directly, it is desirable to derive effective models. In the infinite-particle limit, one may seek to derive a mean-field PDE satisfied by the distributional limit of the empirical measure. In nature, of course, particle numbers are finite, which makes the fluctuations of the dynamics relevant as well. One topic that I am particularly interested in is fluctuating hydrodynamics, in which the fluctuations of a McKean–Vlasov diffusion are described by a scaling-supercritical SPDE called the Dean–Kawasaki equation. Due to the scaling-supercriticality, rigorous justification and well-posedness of fluctuating hydrodynamics models is an active area of research.
[5], [9]

Cross-diffusion systems with entropy structure:  These are (possibly degenerate) strongly coupled parabolic systems. Due to the coupling, the rigorous analysis of these systems can be challenging and is, in general, not amenable to classical energy methods. To recover a priori estimates, often the subclass of cross-diffusion systems that are formally given as the gradient flow of an entropy functional is considered. Such cross-diffusion systems appear very naturally in a variety of contexts; examples include the Shigesada–Kawasaki–Teramoto (SKT) model for population dynamics and the Maxwell–Stefan model for non-Fickian diffusion. Even within this special class of cross-diffusion systems, not much is known concerning the regularity of weak solutions. Previously, together with M. Braukhoff and N. Zamponi, we have been able to derive the first widely applicable partial regularity result in this context, covering, e.g., solutions of the Maxwell–Stefan system and bounded solutions of the SKT model. Since, in this context, full regularity is conjectured, this is a topic that I keep coming back to.
[6]

Singular SPDEs:  These are SPDEs in which the driving noise is so rough that the nonlinearities are not classically defined. In [3] we use Otto and Weber’s framework of modelled distributions to treat the initial value problem for quasilinear parabolic SPDEs driven by additive noise in C^α−2, α ∈ (2/3, 1), a range of comparatively mild roughness within the subcritical regime. The Dean–Kawasaki equation lies beyond this regime altogether, as it is scaling supercritical in the sense of regularity structures. In [9] we do not address its well-posedness; instead, we use it as a tool to describe density fluctuations in weakly interacting particle systems.

Publications

[10] P. Bella, J. Fischer, M. Josien, and C. Raithel. Regularity theorems for random elliptic operators on domains. arXiv preprint: 2604.01209, 2026.

[9] F. Cornalba, J. Fischer, J. Ingmanns, and C. Raithel. Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation. Ann. Probab., 54(1): 155–215, 2026.

[8] P. Bella, J. Fischer, M. Josien, and C. Raithel. Boundary layer estimates in stochastic homogenization. arXiv preprint: 2403.12911, 2024.

[7] M. Josien, C. Raithel, and M. Schäffner. Stochastic homogenization and geometric singularities: a study on corners. SIAM J. Math. Anal., 56(2): 2395–2455, 2024.

[6] M. Braukhoff, C. Raithel, and N. Zamponi. Partial Hölder regularity for solutions of a class of cross-diffusion systems with entropy structure. J. Math. Pures Appl., 166: 30–69, 2022.

[5] E. Daus, M. Ptashnyk, and C. Raithel. Derivation of a fractional cross-diffusion system as the limit of a stochastic many-particle system driven by Lévy noise. J. Differential Equations, 309: 386–426, 2022.

[4] M. Josien and C. Raithel. Quantitative homogenization for the case of an interface between two heterogeneous media. SIAM J. Math. Anal., 53(1): 813–854, 2021.

[3] C. Raithel and J. Sauer. The initial value problem for singular SPDEs via rough paths. arXiv preprint: 2001.00490, 2020. To appear in Stoch. Partial Differ. Equ. Anal. Comput.

[2] J. Fischer and C. Raithel. Liouville principles and a large-scale regularity theory for random elliptic operators on the half-space. SIAM J. Math. Anal., 49(1): 82–114, 2017.

[1] C. Raithel. A large-scale regularity theory for random elliptic operators on the half-space with homogeneous Neumann boundary data. arXiv preprint: 1703.04328, 2017.

Current Teaching

In Winter 2026/27 I am teaching the course Introduction to Stochastic Particle Systems at the TU Wien. All literature for the course will be posted here.

General references

The course is based on the two review articles by Chaintron and Diez:

Review I. L.-P. Chaintron and A. Diez. Propagation of chaos: a review of models, methods and applications. I. Models and methods. Kinet. Relat. Models, 15(6): 895–1015, 2022. arXiv: 2203.00446

Review II. L.-P. Chaintron and A. Diez. Propagation of chaos: a review of models, methods and applications. II. Applications. Kinet. Relat. Models, 15(6): 1017–1173, 2022. arXiv: 2106.14812

Here are some other useful general references:

A.-S. Sznitman. Topics in propagation of chaos. In: École d’Été de Probabilités de Saint-Flour XIX – 1989, Lecture Notes in Math. 1464, pp. 165–251. Springer, Berlin, 1991. DOI: 10.1007/BFb0085169

S. Méléard. Asymptotic behaviour of some interacting particle systems; McKean–Vlasov and Boltzmann models. In: Probabilistic Models for Nonlinear Partial Differential Equations, Lecture Notes in Math. 1627, pp. 42–95. Springer, Berlin, 1996. Google Scholar

L. C. Evans. An Introduction to Stochastic Differential Equations. American Mathematical Society, Providence, RI, 2013. Google Scholar

C. Villani. Optimal Transport: Old and New. Springer, Berlin, 2009. Google Scholar

A. Dembo and O. Zeitouni. Large Deviations Techniques and Applications. 2nd ed., Springer, New York, 1998. Google Scholar

Claudia C. Raithel

Curriculum Vitae

Academic Background

Research Profile

Publications and Preprints

ORCID: 0000-0002-6617-3268

1. P. Bella, J. Fischer, M. Josien, and C. Raithel. Regularity theorems for random elliptic operators on domains. arXiv preprint: 2604.01209, 2026.
2. F. Cornalba, J. Fischer, J. Ingmanns, and C. Raithel. Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation. Ann. Probab., 54(1): 155–215, 2026. DOI: 10.1214/25-AOP1763
3. P. Bella, J. Fischer, M. Josien, and C. Raithel. Boundary layer estimates in stochastic homogenization. arXiv preprint: 2403.12911, 2024.
4. M. Josien, C. Raithel, and M. Schäffner. Stochastic homogenization and geometric singularities: a study on corners. SIAM J. Math. Anal., 56(2): 2395–2455, 2024. DOI: 10.1137/23M1559361
5. M. Braukhoff, C. Raithel, and N. Zamponi. Partial Hölder regularity for solutions of a class of cross-diffusion systems with entropy structure. J. Math. Pures Appl., 166: 30–69, 2022. DOI: 10.1016/j.matpur.2022.07.006
6. E. Daus, M. Ptashnyk, and C. Raithel. Derivation of a fractional cross-diffusion system as the limit of a stochastic many-particle system driven by Lévy noise. J. Differential Equations, 309: 386–426, 2022. DOI: 10.1016/j.jde.2021.11.027
7. M. Josien and C. Raithel. Quantitative homogenization for the case of an interface between two heterogeneous media. SIAM J. Math. Anal., 53(1): 813–854, 2021. DOI: 10.1137/20M1311983
8. C. Raithel and J. Sauer. The initial value problem for singular SPDEs via rough paths. arXiv preprint: 2001.00490, 2020. To appear in Stoch. Partial Differ. Equ. Anal. Comput.
9. J. Fischer and C. Raithel. Liouville principles and a large-scale regularity theory for random elliptic operators on the half-space. SIAM J. Math. Anal., 49(1): 82–114, 2017. DOI: 10.1137/16M1070384
10. C. Raithel. A large-scale regularity theory for random elliptic operators on the half-space with homogeneous Neumann boundary data. arXiv preprint: 1703.04328, 2017.

Awards and Grants

Invited Talks

Teaching Experience

Lecturer

Exercise sessions