Random Walks Systems with Finite Lifetime on \( \mathbb {Z}\)

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• 作者：Elcio Lebensztayn ; Fábio Prates Machado…
• 关键词：Epidemic model ; Frog model ; Global and local survival ; Interacting particle systems ; Random walks
• 刊名：Journal of Statistical Physics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：162
• 期：3
• 页码：727-738
• 全文大小：531 KB
• 参考文献：1.Bertacchi, D., Zucca, F.: Critical behaviors and critical values of branching random walks on multigraphs. J. Appl. Probab. 45, 481–497 (2008)CrossRef MathSciNet MATH
  2.Bertacchi, D., Machado, F., Zucca, F.: Local and global survival for nonhomogeneous random walk systems on Z. Adv. Appl. Probab. 46, 256–278 (2014)CrossRef MathSciNet MATH
  3.Bremaud, P.: Markov chains. Gibbs Fields, Monte Carlo Simulation, and Queues. Texts in Applied Mathematics, vol. 31. Springer, New York (1999)
  4.Gantert, N., Schmidt, P.: Recurrence for the frog model with drift on \(\mathbb{Z}\) . Markov Process. Relat. Fields 15(1), 51–58 (2009)MathSciNet MATH
  5.Kurtz, T.G., Lebensztayn, E., Leichsenring, A.R., Machado, F.P.: Limit theorems for an epidemic model on the complete graph. ALEA 4, 45–55 (2008)MathSciNet MATH
  6.Lebensztayn, E., Machado, F.P., Martinez, M.Z.: Random walks systems with killing on \(\mathbb{Z}\) . Stochastics 80(5), 451–457 (2008)MathSciNet MATH
  7.Lebensztayn, E., Machado, F.P., Martinez, M.Z.: Nonhomogeneous random walks systems on \(\mathbb{Z}\) . J. Appl. Probab. 47(2), 562–571 (2010)CrossRef MathSciNet MATH
  
• 作者单位：Elcio Lebensztayn (1)
  Fábio Prates Machado (2)
  Mauricio Zuluaga Martinez (3)
  
  1. Institute of Mathematics, Statistics and Computer Sciences, UNICAMP, Campinas, Brazil
  2. Institute of Mathematics and Statistics, USP, São Paulo, Brazil
  3. UFERSA, Mossoró, Brazil
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Statistical Physics
  Mathematical and Computational Physics
  Physical Chemistry
  Quantum Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9613

文摘

We consider a non-homogeneous random walks system on \(\mathbb {Z}\) in which each active particle performs a nearest neighbor random walk and activates all inactive particles it encounters up to a total amount of L jumps. We present necessary and sufficient conditions for the process to survive, which means that an infinite number of random walks become activated.