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Quirin Vogel

Publications and source records attributed to Quirin Vogel.

At least 19 recordsLinked to original sources
arXiv2026

Strict-Priority Packet Delay in Switches with Transmit-Ring Buffering

Strict Priority (SP) scheduling is widely used at switch egress to provide low-latency service to high-priority (HP) traffic. Existing deterministic and stochastic latency models typically account for scheduler behavior and packet transmission, but omit a common switch implementation detail: the transmit ring (TXR) between the scheduler and the physical port. Because the switch must prepare the next packet before the current transmission completes, packets already placed in the TXR can further delay HP packets. This changes both the worst-case delay and the per-hop delay distribution of HP packets. This paper identifies this modeling gap, extends standard SP latency models to include the TXR, and validates the revised model through measurements on multiple switches. It also provides a measurement method for estimating the TXR size, a parameter that is often not reported in switch datasheets. The resulting model provides a closer representation of switch behavior for systems that use SP scheduling and require either delay bounds or delay distributions.

cs.NI↗
arXiv2026

Fluctuations for the critical free Bose gas

We study the critical free Bose gas from a probabilistic perspective with a focus on the three-dimensional case. We show that, unlike in the subcritical and supercritical regime, the critical asymptotics depend on the second heat-trace coefficient $a_1$ and hence on the geometry and boundary conditions. For $a_1<0$, long loops occur on the scale $L^2\log L$ and yield Poisson--Dirichlet statistics; for $a_1<0$, such loops are suppressed and the relevant fluctuations are produced by the short-loop bulk. We also derive asymptotics for the partition function, the one-particle reduced density matrix, and loop statistics. The fluctuation limits are governed either by a regularized Fredholm determinant of the Green operator or by Gaussian local central limit theorems, depending on the boundary regime.

math.PR↗
arXiv2026

Improving Network Clock Synchronization by Marking Congestion

Achieving consistent time across devices in distributed systems often involves exchanging timestamped messages over a network. Precise time synchronization is crucial for applications such as cellular networks, industrial automation, and transactional databases. However, delay variation in synchronization packets-often caused by congestion from competing traffic-degrades synchronization accuracy. Detecting whether a packet experienced congestion can help improve synchronization through filtering and statistical methods. We propose an in-network congestion indication and filtering mechanism for synchronization messages used in protocols such as the Network Time Protocol (NTP) and Precision Time Protocol (PTP). Network devices mark packets that experienced queuing, allowing clocks to correct errors caused by varying delays. Our approach requires only simple changes at switches or routers, avoiding deep packet inspection or protocol modifications. The method is backward compatible, using standard but currently unused fields in IP, PTP, or NTP headers. We implement our method on a Tofino P4 target and demonstrate an improvement of over 80% in synchronization performance over a single hop. Moreover, we show that the performance of traditional statistical filters, such as min-RTT and median-delay, is improved by 90% over the one-hop hardware setup. We further demonstrate the effectiveness of our proposed method across multiple hops, both analytically and through simulation. Congestion marking improves the root-mean-squared clock offset estimation error by 30% to 80%, depending on network conditions and filtering techniques.

cs.NI↗
arXiv2025

Phase Transitions in a Particle Model for the Self-Adaptive Response to Cancer Dynamics

In this paper, we present a probabilistic analysis of a dynamical particle model for the self-adaptive immune response to cancer, as proposed by the first author in a previous work. The model is motivated by the interplay between immune surveillance and cancer evolution. We rigorously confirm the sharp phase transition in immune system learning predicted in the original work. Additionally, we compute the expected amount of information acquired by the immune system about cancer cells over time. Our analysis relies on time-reversal techniques.

math.PR↗
arXiv2025

Better Aligned with Survey Respondents or Training Data? Unveiling Political Leanings of LLMs on U.S. Supreme Court Cases

Recent works have shown that Large Language Models (LLMs) have a tendency to memorize patterns and biases present in their training data, raising important questions about how such memorized content influences model behavior. One such concern is the emergence of political bias in LLM outputs. In this paper, we investigate the extent to which LLMs' political leanings reflect memorized patterns from their pretraining corpora. We propose a method to quantitatively evaluate political leanings embedded in the large pretraining corpora. Subsequently we investigate to whom are the LLMs' political leanings more aligned with, their pretrainig corpora or the surveyed human opinions. As a case study, we focus on probing the political leanings of LLMs in 32 US Supreme Court cases, addressing contentious topics such as abortion and voting rights. Our findings reveal that LLMs strongly reflect the political leanings in their training data, and no strong correlation is observed with their alignment to human opinions as expressed in surveys. These results underscore the importance of responsible curation of training data, and the methodology for auditing the memorization in LLMs to ensure human-AI alignment.

cs.CL↗
arXiv2024

Proof of off-diagonal long-range order in a mean-field trapped Bose gas via the Feynman--Kac formula

We consider the non-interacting Bose gas of $N$ bosons in dimension $d\geq 3$ in a trap in a mean-field setting with a vanishing factor $a_N$ in front of the kinetic energy. The choice $a_N=N^{-2/d}$ is the semi-classical setting and was analysed in great detail in a special, interacting case in Deuchert and Seiringer (2021). Using a version of the well-known Feynman--Kac representation and a further representation in terms of a Poisson point process, we derive precise asymptotics for the reduced one-particle density matrix, implying off-diagonal long-range order (ODLRO, a well-known criterion for Bose--Einstein condensation) for $a_N$ above a certain threshold and non-occurrence of ODLRO for $a_N$ below that threshold. In particular, we relate the condensate and its total mass to the amount of particles in long loops in the Feynman--Kac formula, the order parameter that Feynman suggested in Feynman (1953). For $a_N\ll N^{-2/d}$, we prove that all loops have the minimal length one, and for $a_N\gg N^{-2/d}$ we prove 100 percent condensation and identify the distribution of the long-loop lengths as the Poisson--Dirichlet distribution.

math.PR↗
arXiv2024

Large Deviations of Gaussian Neural Networks with ReLU activation

We prove a large deviation principle for deep neural networks with Gaussian weights and at most linearly growing activation functions, such as ReLU. This generalises earlier work, in which bounded and continuous activation functions were considered. In practice, linearly growing activation functions such as ReLU are most commonly used. We furthermore simplify previous expressions for the rate function and provide a power-series expansions for the ReLU case.

stat.ML↗
arXiv2023

Off-diagonal long-range order for the free Bose gas via the Feynman--Kac formula

We consider the path-integral representation of the ideal Bose gas under various boundary conditions. We show that Bose--Einstein condensation occurs at the famous critical density threshold, by proving that its $1$-particle-reduced density matrix exhibits off-diagonal long-range order above that threshold, but not below. Our proofs are based on the well-known Feynman--Kac formula and a representation in terms of a crucial Poisson point process. Furthermore, in the condensation regime, we derive a law of large numbers with strong concentration for the number of particles in short loops. In contrast to the situation for free boundary conditions, where the entire condensate sits in just one loop, for all other boundary conditions we obtain the limiting Poisson--Dirichlet distribution for the collection of the lengths of all long loops. Our proofs are new and purely probabilistic (apart from a standard eigenvalue expansion), using elementary tools like Markov's inequality, Poisson point processes, combinatorial formulas for cardinalities of particular partition sets, and asymptotics for random walks with Pareto-distributed steps.

math.PR↗
arXiv2023

Quenched critical percolation on Galton-Watson trees

We consider critical percolation on a supercritical Galton-Watson tree. We show that, when the offspring distribution is in the domain of attraction of an $\alpha$-stable law for some $\alpha \in (1,2)$, or has finite variance, several annealed properties also hold in a quenched setting. In particular, the following properties hold for the critical root cluster on almost every realisation of the tree: (1) the rescaled survival probabilities converge; (2) the Yaglom limit or its stable analogue hold - in particular, conditioned on survival, the number of vertices at generation $n$ that are connected to the root cluster rescale to a certain (explicit) random variable; (3) conditioned on initial survival, the sequence of generation sizes in the root cluster rescales to a continuous-state branching process. This strengthens some earlier results of Michelen (2019) who proved (1) and (2) in the case where the initial tree has an offspring distribution with all moments finite.

math.PR↗
arXiv2023

An Advanced Tree Algorithm with Interference Cancellation in Uplink and Downlink

In this paper, we propose Advanced Tree-algorithm with Interference Cancellation (ATIC), a variant of binary tree-algorithm with successive interference cancellation (SICTA) introduced by Yu and Giannakis. ATIC assumes that Interference Cancellation (IC) can be performed both by the access point (AP), as in SICTA, but also by the users. Specifically, after every collision slot, the AP broadcasts the observed collision as feedback. Users who participated in the collision then attempt to perform IC by subtracting their transmissions from the collision signal. This way, the users can resolve collisions of degree 2 and, using a simple distributed arbitration algorithm based on user IDs, ensure that the next slot will contain just a single transmission. We show that ATIC reaches the asymptotic throughput of 0.924 as the number of initially collided users tends to infinity and reduces the number of collisions and packet delay. We also compare ATIC with other tree algorithms and indicate the extra feedback resources it requires.

cs.IT↗
arXiv2023

Quantitative bounds for large deviations of heavy tailed random variables

The probability that the sum of independent, centered, identically distributed, heavy-tailed random variables achieves a very large value is asymptotically equal to the probability that there exists a single summand equalling that value. We quantify the error in this approximation. We furthermore characterise of the law of the individual summands, conditioned on the sum being large.

math.PR↗
arXiv2023

Emergence of interlacements from the finite volume Bose soup

We show that, conditioned on the (empirical) particle density exceeding the critical value, the finite volume Bose loop soup converges to the superposition of the Bosonic loop soup (on the whole space) and the Poisson point process of random interlacements. The intensity of the latter is given by the excess density above the critical point. We consider both the free case and the mean field case.

math.PR↗
arXiv2023

Gibbs measures for the repulsive Bose gas

We prove the existence of Gibbs measures for the Feynman representation of the Bose gas with non-negative interaction in the grand-canonical ensemble. Our results are valid for all negative chemical potentials as well as slightly positive chemical potentials. We consider both the Gibbs property of marked points as well as a Markov--Gibbs property of paths.

math.PR↗
arXiv2023

Analysis of d-ary Tree Algorithms with Successive Interference Cancellation

In this article, we calculate the mean throughput, number of collisions, successes, and idle slots for random tree algorithms with successive interference cancellation. Except for the case of the throughput for the binary tree, all the results are new. We furthermore disprove the claim that only the binary tree maximises throughput. Our method works with many observables and can be used as a blueprint for further analysis.

math.PR↗
arXiv2022

Formation of infinite loops for an interacting bosonic loop soup

We compute the limiting measure for the Feynman loop representation of the Bose gas for a non mean-field energy. As predicted in previous works, for high densities the limiting measure gives positive weight to random interlacements, indicating the quantum Bose--Einstein condensation. We prove that in many cases there is a shift in the critical density compared to the free/mean-field case, and that in these cases the density of the random interlacements has a jump-discontinuity at the critical point.

math.PR↗
arXiv2020

Large deviations of the range of the planar random walk on the scale of the mean

We show an upper large deviation bound on the scale of the mean for a symmetric random walk in the plane with finite sixth moment. This result complements the study of Van den Berg, Bolthausen and Den Hollander, where the continuum case of the Wiener Sausage is studied, and in Phetpradap, in which one is restricted to dimension three and higher.

math.PR↗