Asymptotics for logical limit laws: When the growth of the components is in an RT class

DOI10.1090/S0002-9947-03-03299-9zbMath1021.03022OpenAlexW2007080218MaRDI QIDQ4417288

Jason P. Bell, Stanley N. Burris

Publication date: 28 July 2003

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-03-03299-9

zbMATH Keywords

monadic second-order logicasymptotic densityzero-one lawlimit lawratio testSchur's Tauberian theorem

Mathematics Subject Classification ID

Asymptotic results on counting functions for algebraic and topological structures (11N45) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20) Asymptotic enumeration (05A16) Model theory of finite structures (03C13) Additive number theory; partitions (11P99) Generalized primes and integers (11N80) Connections of number theory and logic (11U99)

Related Items (8)

Deterministic and Stochastic Becker–Döring Equations: Past and Recent Mathematical Developments ⋮ Random graphs from a weighted minor-closed class ⋮ Asymptotic density in quasi-logarithmic additive number systems ⋮ Clustering in coagulation-fragmentation processes, random combinatorial structures and additive number systems: Asymptotic formulae and limiting laws ⋮ Partition identities. II: The results of Bateman and Erdős ⋮ Dirichlet series whose partial sums of coefficients have regular variation ⋮ Limit shapes of Gibbs distributions on the set of integer partitions: The expansive case ⋮ On the variance of the number of occupied boxes

Cites Work

• A logical approach to asymptotic combinatorics I. First order properties
• The equilibrium behavior of reversible coagulation-fragmentation processes
• Asymptotics for the probability of connectedness and the distribution of number of components
• A logical approach to asymptotic combinatorics. II: Monadic second-order properties
• Sufficient conditions for zero-one laws
• "Factorisatio numerorum" in arithmetical semigroups
• Asymptotic Methods in Enumeration
• Fine Spectra and Limit Laws, II First-Order 0–1 Laws
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