Clustering in coagulation-fragmentation processes, random combinatorial structures and additive number systems: Asymptotic formulae and limiting laws

DOI10.1090/S0002-9947-04-03617-7zbMath1062.60097arXivmath/0207265OpenAlexW1627845523MaRDI QIDQ4654155

Gregory A. Freiman, Boris L. Granovsky

Publication date: 1 March 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0207265

zbMATH Keywords

clusteringrandom combinatorial structuresadditive number systems

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Exact enumeration problems, generating functions (05A15) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Asymptotic enumeration (05A16) Tauberian theorems (40E05)

Related Items (6)

Coagulation Processes with Gibbsian Time Evolution ⋮ Deterministic and Stochastic Becker–Döring Equations: Past and Recent Mathematical Developments ⋮ Universality of the limit shape of convex lattice polygonal lines ⋮ Random combinatorial structures: the convergent case ⋮ Limit shapes of Gibbs distributions on the set of integer partitions: The expansive case ⋮ On time dynamics of coagulation-fragmentation processes

Cites Work

• Asymptotic formula for a partition function of reversible coagulation-fragmentation processes
• The steady-state distributions of coagulation-fragmentation processes
• Convergence to equilibrium in a system of reacting polymers
• Existence of gelling solutions for coagulation-fragmentation equations
• Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists
• The equilibrium behavior of reversible coagulation-fragmentation processes
• Smoluchowski's coagulation equation: Uniqueness, nonuniqueness and a hydrodynamic limit for the stochastic coalescent
• Independent process approximations for random combinatorial structures
• A Poisson approximation for the Dirichlet law, the Ewens sampling formula and the Griffiths-Engen-McCloskey law by the Stein-Chen coupling method
• Construction of Markovian coalescents
• Logarithmic combinatorial structures: A probabilistic approach
• Size of the largest cluster under zero-range invariant measures
• Stochastic particle approximations for Smoluchowski's coagulation equation
• Cluster coagulation
• A Local Limit Theorem for Random Strict Partitions
• Sufficient conditions for zero-one laws
• Local Limit Theorems for Sums of Power Series Distributed Random Variables and for the Number of Components in Labelled Relational Structures
• Emergence of the giant component in special Marcus-Lushnikov processes
• Asymptotics for logical limit laws: When the growth of the components is in an RT class
• Regularly varying functions
• The discrete coagulation equations with collisional breakage.
• Homogeneous fragmentation processes
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Clustering in coagulation-fragmentation processes, random combinatorial structures and additive number systems: Asymptotic formulae and limiting laws