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Graph limit for interacting particle systems on weighted random graphs.

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Title: Graph limit for interacting particle systems on weighted random graphs.
Authors: Ayi, Nathalie1 (AUTHOR) nathalie.ayi@sorbonne-universite.fr, Pouradier Duteil, Nastassia2 (AUTHOR) nastassia.pouradier_duteil@sorbonne-universite.fr
Source: Mathematical Models & Methods in Applied Sciences. May2026, Vol. 36 Issue 5, p1129-1174. 46p.
Subjects: Weighted graphs, Limit theorems, Stochastic processes, Mathematical analysis, Graph theory, Numerical analysis
Abstract: In this paper, we study the large-population limit of interacting particle systems posed on weighted random graphs. In that aim, we introduce a general framework for the construction of weighted random graphs, generalizing the concept of graphons. We prove quantitative convergence results in probability, as the number of particles tends to infinity, of the finite-dimensional system toward the solution of a deterministic graph limit equation. In this limit equation, the graphon prescribing the interaction is given by the first moment of the weighted random graph law. We also study interacting particle systems posed on switching weighted random graphs, which are obtained by resetting the weighted random graph at regular time intervals. We reveal the interplay between the large-population limit and the switching time. In particular, we show that for a fixed switching time, these systems converge as the number of particles tends to infinity to the same graph limit equation, in which the interaction is prescribed by the constant-in-time first moment of the weighted random graph law. Our results are illustrated by some numerical simulations. [ABSTRACT FROM AUTHOR]
Copyright of Mathematical Models & Methods in Applied Sciences is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Graph limit for interacting particle systems on weighted random graphs.
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  Data: <searchLink fieldCode="AR" term="%22Ayi%2C+Nathalie%22">Ayi, Nathalie</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> nathalie.ayi@sorbonne-universite.fr</i><br /><searchLink fieldCode="AR" term="%22Pouradier+Duteil%2C+Nastassia%22">Pouradier Duteil, Nastassia</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> nastassia.pouradier_duteil@sorbonne-universite.fr</i>
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  Data: <searchLink fieldCode="JN" term="%22Mathematical+Models+%26+Methods+in+Applied+Sciences%22">Mathematical Models & Methods in Applied Sciences</searchLink>. May2026, Vol. 36 Issue 5, p1129-1174. 46p.
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  Data: <searchLink fieldCode="DE" term="%22Weighted+graphs%22">Weighted graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Limit+theorems%22">Limit theorems</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink>
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  Data: In this paper, we study the large-population limit of interacting particle systems posed on weighted random graphs. In that aim, we introduce a general framework for the construction of weighted random graphs, generalizing the concept of graphons. We prove quantitative convergence results in probability, as the number of particles tends to infinity, of the finite-dimensional system toward the solution of a deterministic graph limit equation. In this limit equation, the graphon prescribing the interaction is given by the first moment of the weighted random graph law. We also study interacting particle systems posed on switching weighted random graphs, which are obtained by resetting the weighted random graph at regular time intervals. We reveal the interplay between the large-population limit and the switching time. In particular, we show that for a fixed switching time, these systems converge as the number of particles tends to infinity to the same graph limit equation, in which the interaction is prescribed by the constant-in-time first moment of the weighted random graph law. Our results are illustrated by some numerical simulations. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Mathematical Models & Methods in Applied Sciences is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1142/S0218202526500223
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      – Code: eng
        Text: English
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        PageCount: 46
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    Subjects:
      – SubjectFull: Weighted graphs
        Type: general
      – SubjectFull: Limit theorems
        Type: general
      – SubjectFull: Stochastic processes
        Type: general
      – SubjectFull: Mathematical analysis
        Type: general
      – SubjectFull: Graph theory
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      – SubjectFull: Numerical analysis
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      – TitleFull: Graph limit for interacting particle systems on weighted random graphs.
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              M: 05
              Text: May2026
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              Y: 2026
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