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Topics of Stochastic Algebraic Topology

Jahangardi, Mostafa | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 52194 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Jafari, Amir
  7. Abstract:
  8. Stochastic Algebraic Topology studies stochastic or less known spaces that depend on many random variables from the perspective of algebra. Examples of such spaces included random graphs of Erdos and Renyi and random simplicial spaces of higher dimension . In this thesis , we study algebraic aspects of these spaces such as homotopy groups and homology groups from probabilistic point of view , when the number of vertices of these spaces tend to infinity . The study of these spaces have a lot of applications, since the data for a given space can be incomplete . They are also used in big system structures. We have given a collection of new results in stochastic algebraic topology of two dimensional random simplicial spaces
  9. Keywords:
  10. Random Group ; Random Complex ; Stochastic Topology ; Algebraic Connectivity

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