Do the rich get richer? Mathematical models for real-world networks

Instantáneas de la actualidad matemática desde Oberwolfach

Do the rich get richer? Mathematical models for real-world networks

Networks can be found all around us. From the friendships we form, both in person and online, to the websites we visit on the Internet, and the telephones we use to send messages and make phone calls. Understanding the behavior and structure of these networks can be a difficult task. Mathematicians use models of such complex real-world networks to provide novel insights from an analytical point of view. In this snapshot, we take a look at why mathematics can be useful in understanding networks and discuss interesting recent developments in the study of a popular class of models known as preferential attachment models, which try to explain why the rich get richer.

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Área matemática

Teoría de la probabilidad y Estadística

Relaciones con otros campos

Informática
Ingeniería y Tecnología
Humanidades y Ciencias sociales
Física

Autor(es)

Bas Lodewijks

Licencia

DOI (Identificador de objetos digitales)

10.14760/SNAP-2026-010-EN

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snapshot-2026-010.pdf

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snapshots: overview

Bas Lodewijks
Do the rich get richer? Mathematical models for real-world networks
Glenn Shafer
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Why oscillation counts: Diophantine approximation, geometry, and the Fourier transform
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Is there a smooth lattice polytope which does not have the integer decomposition property?
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Brauer’s problems: 60 years of legacy
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Trisections of four-dimensional spaces
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The five Platonic solids and their connection to root systems
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Five ways to spell ADE
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Convex polytopes and linear programs
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Finite geometries: pure mathematics close to applications
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Quantum symmetry
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Fadoua Balabdaoui, Yulia Kulagina
The Enigma behind the Good–Turing formula
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Reflections on hyperbolic space
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Ultrafilter methods in combinatorics
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Invitation to quiver representation and Catalan combinatorics
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Rotating needles, vibrating strings, and Fourier summation
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Quantum symmetry
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Determinacy versus indeterminacy
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Vertex-to-Self Trajectories on the Platonic Solids
Gianluca Finocchio
Random matrix theory: Dyson Brownian motion
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The Interaction of Curvature and Topology
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Formation Control and Rigidity Theory
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Algebra, matrices, and computers
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Positive Scalar Curvature and Applications
Hector Pasten
Diophantine equations and why they are hard
Martin Buhmann, Janin Jäger
On radial basis functions
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Snake graphs, perfect matchings and continued fractions
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Estimating the volume of a convex body
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Mixed volumes and mixed integrals
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Topological recursion
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Marco Radeschi
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Christian Engwer, Markus Knappitsch
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Laurent Bartholdi
Profinite groups
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Nikolai Nowaczyk
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Prime Tuples in Function Fields
Rafael Guglielmetti, Matthieu Jacquemet
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Manfred Deistler, Andreas Graef
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Robert Altmann, Jan Heiland
Wie steuert man einen Kran?
Anthony T Patera, Karsten Urban
High performance computing on smartphones
Eugenio Giannelli, Jay Taylor
Symmetry and characters of finite groups
Maria Dostert, Stefan Krupp, Jan Hendrick Rolfes
Das Problem der Kugelpackung
Tomasz Szemberg, Justyna Szpond
On the containment problem
Éric Fusy
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Magnus Egerstedt
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Ulrich Krähmer
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Domino tilings of the Aztec Diamond
Sebastian Funk
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Quantum diffusion
Amanda Swan, Albert Murtha
Modelling the spread of brain tumours
J. Marron
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Christopher Sangwin
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Victoria Powers
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Valentina Kiritchenko, Evgeny Smirnov, Vladlen Timorin
Ideas of Newton-Okounkov bodies
Ben Schweizer
Darcy’s law and groundwater flow modelling
Raluca Eftimie
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Tom Solomon
Chaos and chaotic fluid mixing
Thorsten Holm
Friezes and tilings
George Willis
Zero-dimensional symmetry
Christine Breiner
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Diana Davis
Billiards and flat surfaces
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Alain Valette
The Kadison-Singer problem
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Harald Helfgott
The ternary Goldbach Problem
Wolfgang Lerche
Matrixfaktorisierungen
John E. McCarthy
Dirichlet Series

Área matemática

Álgebra y Teoría de números
Análisis
Didáctica y Educación
Matemática discreta y Fundamentos
Geometría y Topología
Cálculo numérico y científico
Teoría de la probabilidad y Estadística

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Química y Ciencias de la Tierra
Informática
Ingeniería y Tecnología
Finanzas
Humanidades y Ciencias sociales
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Reflexiones sobre la matemática

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