Spectral properties of evolutionary operators in branching random walk models

DOI10.1134/S0001434612070139zbMath1269.82057OpenAlexW1995073513MaRDI QIDQ1938635

E. B. Yarovaya

Publication date: 22 February 2013

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434612070139

zbMATH Keywords

positive eigenvaluebranching random walkpseudodifference operatorequations in Banach spacessymmetrizable operator

Mathematics Subject Classification ID

Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Continuous-time Markov processes on discrete state spaces (60J27)

Related Items (22)

Strong and weak convergence of the population size in a supercritical catalytic branching process ⋮ A weakly supercritical mode in a branching random walk ⋮ On the Number of Positive Eigenvalues of the Evolutionary Operator of Branching Random Walk ⋮ Branching random walk with receding sources ⋮ Simulation of branching random walks on a multidimensional lattice ⋮ Spectral Asymptotics of a Supercritical Branching Random Walk ⋮ Branching random walks with alternating sign intensities of branching sources ⋮ Branching processes with lattice spatial dynamics and a finite set of particle generation centers ⋮ The structure of the positive discrete spectrum of the evolution operator arising in branching random walks ⋮ Moment Asymptotics of Population Size of Particles at Vertices for a Supercritical Branching Random Walk on a Periodic Graph ⋮ Positive discrete spectrum of the evolutionary operator of supercritical branching walks with heavy tails ⋮ Asymptotic behavior of the mean number of particles for a branching random walk on the lattice \(\mathbb{Z}^d\) with periodic sources of branching ⋮ Population structure inside the propagation front of a branching random walk with finitely many centers of particle generation ⋮ Asymptotic behavior of branching random walks on some two-dimensional lattices ⋮ Large deviations for a symmetric branching random walk on a multidimensional lattice ⋮ Stationary distributions in Kolmogorov-Petrovski- Piskunov-type models with an infinite number of particles ⋮ Operators Satisfying the Schur Condition and their Applications to the Branching Random Walks ⋮ On the mean number of particles of a branching random walk on \(\mathbb{Z}^d\) with periodic sources of branching ⋮ Operator equations of branching random walks ⋮ Branching Random Walks on $Z^d$ with Periodic Branching Sources ⋮ A Limit Theorem for Supercritical Random Branching Walks with Branching Sources of Varying Intensity ⋮ Influence of the Configuration of Particle Generation Sources on the Behavior of Branching Walks: A Case Study

Cites Work

• Branching random walk in a catalytic medium. I: Basic equations
• Asymptotics of branching symmetric random walk on the lattice with a single source
• A limit theorem for a supercritical branching random walk on $ \mathbb Z^d$ with a single source
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