Mathematics, Volume 10, Issue 21
2022 November-1 - 245 articles
Cover Story: A diffusion-taking value in probability measures on undirected graphs is studied, and applications are presented. The masses on vertices satisfy the stochastic differential equation dxi = ∑j∈N(i) \({\sqrt{x_{i} x_{j}}}\) dBij, where {Bij} are independent Brownian motions with skew symmetry and N(i) is the neighbour of the vertex i. A dual Markov chain of the diffusion on ordered non-negative integer partitions is effectively used. A chain at a state a = (a1, ..., a|V|), where ai is the number of particles at i, jumps to a − ei + ej with rate ai(ai − 1)/2 if i and j are adjacent. For this cycle graph, possible transitions from (0, 2, 0, 1), a partition of 3, are shown in the right. A collision occurs between two particles in vertex 2, and one of them moves to one of the adjacent vertices: 1 or 3. View this paper - Issues are regarded as officially published after their release is announced to the table of contents alert mailing list .
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