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Tobias Schmidt

Publications and source records attributed to Tobias Schmidt.

At least 19 recordsLinked to original sources
arXiv2026

Conditioned Brownian motion and local equivalence of path ensembles

We study Brownian motion in R^d conditioned so that the time average of a continuous confining potential remains below a fixed level. On every fixed initial time interval, we prove that the conditioned process converges in total variation to the ground-state diffusion associated with a suitable Schrödinger operator. We also obtain sharp asymptotics for the probability of the conditioning event, including bounded perturbations of the constraint. The proof is based on a local limit theorem for the corresponding Feynman-Kac measures. Our results extend the previously known one-dimensional quadratic case to arbitrary finite dimension and a broad class of confining potentials, therefore resolving a conjecture of Aurzada, Lifshits and Schickentanz. The presented approach also works when Brownian motion is replaced by suitable reversible Markov processes, including multidimensional Ornstein-Uhlenbeck processes, CIR processes and continuous-time Markov chains.

math.PR↗
arXiv2026

Recent development in high-precision high-fidelity spectrographs for exoplanet research and characterization

High-precision high-fidelity spectrographs are the most powerful instruments for exoplanets detection and characterization. The sub-m/s radial-velocity precision, required to detect Earth-mass exoplanets, necessitates tackling all the sources of instrumental and stellar instabilities. We present the new high-precision high-fidelity spectrographs ESPRESSO, NIRPS, ANDES and RISTRETTO designed, developed, and operated with support of PlanetS.

astro-ph.IM↗
arXiv2026

The Uncertain Policy Price of Scaling Direct Air Capture

Direct air carbon capture and storage (DACCS) is a promising CO2 removal technology, but its deployment at scale remains speculative. Yet, its technological, economic, and policy-related uncertainties have often been overlooked in mitigation pathways. This paper conducts the first uncertainty quantification and global sensitivity analysis of DACCS on technological, market, financial and public support drivers, using a detailed-process Integrated Assessment Model and newly developed sensitivity algorithms. We find that DACCS deployment exhibits a fat-tailed distribution: most scenarios show modest technology uptake, but there is a small but non-zero probability (4-6%) of achieving gigaton-scale removals by mid-century. Scaling DACCS to gigaton levels requires subsidies that always exceed 200-330 USD/tCO2 and are sustained for decades, resulting in a public support programme of 900-3000 USD Billions. Such an effort pays back by mid-century, but only if accompanied by strong emission reduction policies. These findings highlight the critical role of climate policies in enabling a robust and economically sustainable CO2 removal strategy.

stat.AP↗
arXiv2026

On Anti-Confinement Estimates for Self-Repelling Random Walks

We study a class of $d$-dimensional random walks, including the two-dimensional simple random walk, reweighted by a self-repelling Gibbsian pair potential. We prove lower bounds on the diffusion constant for short-range interactions, and superdiffusive behavior in case the interaction is sufficiently long-range. Finally, we show that in the superdiffusive regime, faster temporal decay can be compensated by stronger spatial repulsion and vice-versa. Our technique combines GKS-based correlation inequalities on path space with recursive multi-scale estimates.

math.PR↗
arXiv2026

Pro-p Iwahori Hecke algebras and the dual Vinberg monoid

Let G be a split reductive group over the integers, F a p-adic local field with residue field Fq. We relate the pro-p-Iwahori Hecke algebra H of G(F) over Fq to the Vinberg monoid of the dual group and study this relation. As an application, in the GL(n)-case and for F/Qp unramified, we derive a parametrization of SpecZ by semisimple n-dimensional representations of the absolute Galois group of F, generalizing the known case n = 2. Here Z denotes the center of H.

math.RT↗
arXiv2026

Mean-Field Control on Sparse Graphs: From Local Limits to GNNs via Neighborhood Distributions

Mean-field control (MFC) offers a scalable solution to the curse of dimensionality in multi-agent systems but traditionally hinges on the restrictive assumption of exchangeability via dense, all-to-all interactions. In this work, we bridge the gap to real-world network structures by proposing a rigorous framework for MFC on large sparse graphs. We redefine the system state as a probability measure over decorated rooted neighborhoods, effectively capturing local heterogeneity. Our central contribution is a theoretical foundation for scalable reinforcement learning in this setting. We prove horizon-dependent locality: for finite-horizon problems, an agent's optimal policy at time t depends strictly on its (T-t)-hop neighborhood. This result renders the infinite-dimensional control problem tractable and underpins a novel Dynamic Programming Principle (DPP) on the lifted space of neighborhood distributions. Furthermore, we formally and experimentally justify the use of Graph Neural Networks (GNNs) for actor-critic algorithms in this context. Our framework naturally recovers classical MFC as a degenerate case while enabling efficient, theoretically grounded control on complex sparse topologies.

cs.MA↗
arXiv2025

Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actions

We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs $(\mathbf{y}, g \cdot \mathbf{y})$, where $g$ is drawn from a finite group acting on the data. Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps -- without relying on group-specific inductive biases. We validate our approach on the infinite dSprites dataset with structured transformations defined by the finite group $G:= (R_m \times \mathbb{Z}_n \times \mathbb{Z}_n)$, combining discrete rotations and periodic translations. The resulting embeddings exhibit high-fidelity equivariance, with group operations faithfully reproduced in latent space. On synthetic data, we further validate the approach on the non-abelian orthogonal group $O(n)$ and the general linear group $GL(n)$. We also provide a theoretical proof for identifiability. While broad evaluation across diverse group types on real-world data remains future work, our results constitute the first successful demonstration of general-purpose encoder-only equivariant learning from group action observations alone, including non-trivial non-abelian groups and a product group motivated by modeling affine equivariances in computer vision.

cs.LG↗
arXiv2025

Narrative Shift Detection: A Hybrid Approach of Dynamic Topic Models and Large Language Models

With rapidly evolving media narratives, it has become increasingly critical to not just extract narratives from a given corpus but rather investigate, how they develop over time. While popular narrative extraction methods such as Large Language Models do well in capturing typical narrative elements or even the complex structure of a narrative, applying them to an entire corpus comes with obstacles, such as a high financial or computational cost. We propose a combination of the language understanding capabilities of Large Language Models with the large scale applicability of topic models to dynamically model narrative shifts across time using the Narrative Policy Framework. We apply a topic model and a corresponding change point detection method to find changes that concern a specific topic of interest. Using this model, we filter our corpus for documents that are particularly representative of that change and feed them into a Large Language Model that interprets the change that happened in an automated fashion and distinguishes between content and narrative shifts. We employ our pipeline on a corpus of The Wall Street Journal news paper articles from 2009 to 2023. Our findings indicate that a Large Language Model can efficiently extract a narrative shift if one exists at a given point in time, but does not perform as well when having to decide whether a shift in content or a narrative shift took place.

cs.CL↗
arXiv2025

Identifying economic narratives in large text corpora -- An integrated approach using Large Language Models

As interest in economic narratives has grown in recent years, so has the number of pipelines dedicated to extracting such narratives from texts. Pipelines often employ a mix of state-of-the-art natural language processing techniques, such as BERT, to tackle this task. While effective on foundational linguistic operations essential for narrative extraction, such models lack the deeper semantic understanding required to distinguish extracting economic narratives from merely conducting classic tasks like Semantic Role Labeling. Instead of relying on complex model pipelines, we evaluate the benefits of Large Language Models (LLMs) by analyzing a corpus of Wall Street Journal and New York Times newspaper articles about inflation. We apply a rigorous narrative definition and compare GPT-4o outputs to gold-standard narratives produced by expert annotators. Our results suggests that GPT-4o is capable of extracting valid economic narratives in a structured format, but still falls short of expert-level performance when handling complex documents and narratives. Given the novelty of LLMs in economic research, we also provide guidance for future work in economics and the social sciences that employs LLMs to pursue similar objectives.

econ.GN↗
arXiv2025

Self-supervised contrastive learning performs non-linear system identification

Self-supervised learning (SSL) approaches have brought tremendous success across many tasks and domains. It has been argued that these successes can be attributed to a link between SSL and identifiable representation learning: Temporal structure and auxiliary variables ensure that latent representations are related to the true underlying generative factors of the data. Here, we deepen this connection and show that SSL can perform system identification in latent space. We propose dynamics contrastive learning, a framework to uncover linear, switching linear and non-linear dynamics under a non-linear observation model, give theoretical guarantees and validate them empirically.

stat.ML↗
arXiv2025

Enhanced binding for a quantum particle coupled to scalar quantized field

Enhanced binding of a quantum particle coupled to a quantized field means that the Hamiltonian of the particle alone does not have a bound state, while the particle-field Hamiltonian does. For the Pauli--Fierz model, this is usually shown via the binding condition, which works less well in the case of a linear coupling to a scalar field. In particular, the case of a single particle linearly coupled to a scalar field has been open so far. Using a method relying on functional integrals and the Gaussian correlation inequality, we obtain enhanced binding for this case. From a statistical mechanics point of view, our result describes a localization phase transition (in the strength of the pair potential) for a Brownian motion subject to an external and an attractive pair potential.

math-ph↗
arXiv2024

Explicit bounds for a Gaussian decomposition Lemma of Sellke

In arXiv:2212.14023 a decomposition of Gaussian measures on finite-dimensional spaces was introduced, which turned out to be a central technical tool to improve currently known bounds on a long standing conjecture in statistical mechanics called the Polaron problem. This note slightly generalizes this decomposition and provides numerical values for all occurring constants.

math.PR↗
arXiv2023

Mean square displacement of Brownian paths perturbed by bounded pair potentials

We study Brownian paths perturbed by semibounded pair potentials and prove upper bounds on the mean square displacement. As a technical tool we derive infinite dimensional versions of key inequalities that were first used in [Sellke; arXiv:2212.14023] in order to study the effective mass of the Fröhlich polaron.

math.PR↗
arXiv2023

Lubin-Tate moduli space of semisimple mod p Galois representations for GL_2 and Hecke modules

Let $p$ be an odd prime. Let $F$ be a non-archimedean local field of residue characteristic $p$, and let $\mathbb{F}_q$ be its residue field. Let $\mathcal{H}^{(1)}_{\mathbb{F}_q}$ be the pro-$p$-Iwahori-Hecke algebra of the $p$-adic group ${\textrm GL_2}(F)$ with coefficients in $\mathbb{F}_q$, and let $Z(\mathcal{H}^{(1)}_{\mathbb{F}_q})$ be its center. We define a scheme $X(q)_{\mathbb{F}_q}$ whose geometric points parametrize the semisimple two-dimensional Galois representations of ${\textrm Gal}(\overline{F}/F)$ over $\overline{\mathbb{F}}_q$. Then we construct a morphism from the spectrum of $Z(\mathcal{H}^{(1)}_{\mathbb{F}_q})$ to $X(q)_{\mathbb{F}_q}$ generalizing the morphism appearing in \cite{PS2} for $F=\mathbb{Q}_p$. In the case $F/\mathbb{Q}_p$, we show that the induced map from Hecke modules to Galois representations, when restricted to supersingular modules, coincides with Grosse-Klönne's bijection \cite{GK18}. For this, we determine the Lubin-Tate $(φ,Γ)$-modules associated to absolutely irreducible Galois representations.

math.NT↗
arXiv2023

Robustness of Graph Neural Networks at Scale

Graph Neural Networks (GNNs) are increasingly important given their popularity and the diversity of applications. Yet, existing studies of their vulnerability to adversarial attacks rely on relatively small graphs. We address this gap and study how to attack and defend GNNs at scale. We propose two sparsity-aware first-order optimization attacks that maintain an efficient representation despite optimizing over a number of parameters which is quadratic in the number of nodes. We show that common surrogate losses are not well-suited for global attacks on GNNs. Our alternatives can double the attack strength. Moreover, to improve GNNs' reliability we design a robust aggregation function, Soft Median, resulting in an effective defense at all scales. We evaluate our attacks and defense with standard GNNs on graphs more than 100 times larger compared to previous work. We even scale one order of magnitude further by extending our techniques to a scalable GNN.

cs.LG↗