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Information-theoretic quantities have received significant attention as system-independent measures of correlations in many-body quantum systems, e.g., as universal order parameters of synchronization. In this work, we present a method to…

Quantum Physics · Physics 2025-11-24 Krzysztof Ptaszynski , Maciej Chudak , Massimiliano Esposito

Fisher-KPP equation is proved to be the scaling limit of a system of Brownian particles with local interaction. Particles proliferate and die depending on the local concentration of other particles. Opposite to discrete models, controlling…

Probability · Mathematics 2021-04-13 Franco Flandoli , Ruojun Huang

We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface $I$. This system can be used to model the transport of positive and negative charges in a…

Probability · Mathematics 2021-01-12 Zhen-Qing Chen , Wai-Tong Fan

We derive upper bounds on the quantum Fisher information in interferometry with $N$ subsystems, e.g. two-level atoms or Gaussian modes, in the presence of arbitrarily correlated Gaussian dephasing including independent and collective…

Quantum Physics · Physics 2014-03-06 Katarzyna Macieszczak

In this paper, we consider graphon particle systems with heterogeneous mean-field type interactions and the associated finite particle approximations. Under suitable growth (resp. convexity) assumptions, we obtain uniform-in-time…

Probability · Mathematics 2022-10-21 Erhan Bayraktar , Ruoyu Wu

The Fisher-Rao metric from Information Geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of Information Geometry to study more general phase transitions in…

Statistical Mechanics · Physics 2016-05-04 Omri Har Shemesh , Rick Quax , Alfons G. Hoekstra , Peter M. A. Sloot

We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…

Analysis of PDEs · Mathematics 2025-10-09 Vincent Bansaye , Alexandre Bertolino , Ayman Moussa

We formulate the planar `large N limit' of matrix models with a continuously infinite number of matrices directly in terms of U(N) invariant variables. Non-commutative probability theory, is found to be a good language to describe this…

High Energy Physics - Theory · Physics 2014-11-18 A. Agarwal , L. Akant , G. S. Krishnaswami , S. G. Rajeev

The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we…

Quantum Physics · Physics 2012-11-21 B. M. Escher , L. Davidovich , N. Zagury , R. L. de Matos Filho

We consider the processing of statistical samples $X\sim P_\theta$ by a channel $p(y|x)$, and characterize how the statistical information from the samples for estimating the parameter $\theta\in\mathbb{R}^d$ can scale with the mutual…

Information Theory · Computer Science 2021-07-12 Leighton Pate Barnes , Ayfer Ozgur

In this contribution, quantum Fisher information is utilized to estimate the parameters of a central qubit interacting with a single-spin qubit. The effect of the longitudinal, transverse and the rotating strengths of the magnetic field on…

Quantum Physics · Physics 2018-04-04 N. Metwally

We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…

Statistics Theory · Mathematics 2024-03-05 Rémy Degenne , Timothée Mathieu

Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…

Analysis of PDEs · Mathematics 2023-06-13 Marie Doumic , Sophie Hecht , Benoit Perthame , Diane Peurichard

We investigated quantum critical behaviours in the non-equilibrium steady state of a $XXZ$ spin chain with boundary Markovian noise using the Fisher information. The latter represents the distance between two infinitesimally close states,…

Statistical Mechanics · Physics 2017-09-19 Ugo Marzolino , Tomaž Prosen

The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…

Analysis of PDEs · Mathematics 2019-06-05 Antonin Della Noce , Amélie Mathieu , Paul-Henry Cournède

We study the existence of the maximal quantum Fisher information matrix in multi-parameter quantum estimation, which bounds the ultimate precision limit. We show that when the maximal quantum Fisher information matrix exists, it can be…

Quantum Physics · Physics 2017-08-02 Yu Chen , Haidong Yuan

We derive a Fisher matrix for the parameters characterising a population of gravitational-wave events. This provides a guide to the precision with which population parameters can be estimated with multiple observations, which becomes…

General Relativity and Quantum Cosmology · Physics 2022-12-14 Jonathan R. Gair , Andrea Antonelli , Riccardo Barbieri

The mean-field limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diffusion equations, modeling the segregation of populations.…

Analysis of PDEs · Mathematics 2019-09-04 Li Chen , Esther S. Daus , Ansgar Jüngel

The quantum Cram\'er-Rao bound sets a fundamental limit on the accuracy of unbiased parameter estimation in quantum systems, relating the uncertainty in determining a parameter to the inverse of the quantum Fisher information. We…

We study the large-population limit of interacting particle systems evolving on adaptive dynamical networks, motivated in particular by models of opinion dynamics. In such systems, agents interact through weighted graphs whose structure…

Analysis of PDEs · Mathematics 2026-01-13 Nathalie Ayi