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Biased Random Walk On Galton-Watson Tree With Leaves

Khaniha, Sayeh | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 50827 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Haji Mirsadeghi, Mir Omid
  7. Abstract:
  8. We consider a biased random walk Xn on a Galton-watson tree with leaves in the subballistic regime. We prove that there exists an explicit constant ϒ = ϒ(β) ε (0,1),such that |Xn| is of order n. If Δn be the hitting time of level n, we prove that Δn{n1{ is tight. More ever we show thatΔn{n1{ does not converge in law. We prove that along the sequences npkq Xk\ , Δn{n1{ converges to certain infinity divisible laws. Key tools for the proof are the classical Harris decomposition for Galton-Watson trees, a new variant of regeneration times and the careful analysis of triangular arrays of i.i.d. random variables
  9. Keywords:
  10. Branching Proccess ; Random Walk ; Random Walk on Random Environment ; Electrical Network ; Infinitly Divisible Distribution

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