Spectral analysis of random-to-random Markov chains
نویسندگان
چکیده
منابع مشابه
Random walks and Markov chains
This lecture discusses Markov chains, which capture and formalize the idea of a memoryless random walk on a finite number of states, and which have wide applicability as a statistical model of many phenomena. Markov chains are postulated to have a set of possible states, and to transition randomly from one state to a next state, where the probability of transitioning to a particular next state ...
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Let G = (V,E) be a connected, undirected graph with n vertices and m edges. For a vertex v ∈ V , Γ(v) denotes the set of neighbors of v in G. A random walk on G is the following process, which occurs in a sequence of discrete steps: starting at a vertex v0, we proceed at the first step to a random edge incident on v0 and walking along it to a vertex v1, and so on. ”Random chosen neighbor” will ...
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Let $G$ be a molecular graph with vertex set $V(G)$, $d_G(u, v)$ the topological distance between vertices $u$ and $v$ in $G$. The Hosoya polynomial $H(G, x)$ of $G$ is a polynomial $sumlimits_{{u, v}subseteq V(G)}x^{d_G(u, v)}$ in variable $x$. In this paper, we obtain an explicit analytical expression for the expected value of the Hosoya polynomial of a random benzenoid chain with $n$ hexagon...
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متن کاملLecture 7: Markov Chains and Random Walks
A transition probability Pij corresponds to the probability that the state at time step t+1 will be j, given that the state at time t is i. Therefore, each row in the matrix M is a distribution and ∀i, j ∈ SPij ≥ 0 and ∑ j Pij = 1. Let the initial distribution be given by the row vector x ∈ R, xi ≥ 0 and ∑ i xi = 1. After one step, the new distribution is xM. It is easy to see that xM is again ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2018
ISSN: 0001-8708
DOI: 10.1016/j.aim.2017.10.034