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Given a random walk a method is presented to produce a matrix of transition probabilities that is consistent with that random walk. The method is a kind of reverse application of the usual ergodicity and is tested by using a transition matrix to produce a path and then using that path to create the estimate. The two matrices and their predictions are then compared. A variety of situations test the method, random matrices, metastable configurations (for which ergodicity often does not apply) and explicit violation of detailed balance.
A random matrix model of black holes is given based on analysis of Gaussian complex ensembles, based on the generalization of chRMT of QCD. Spacetime freedoms are incorporated in terms of eigenvalues of the ensemble. Classical observables of black ho
We define a correlated random walk (CRW) induced from the time evolution matrix (the Grover matrix) of the Grover walk on a graph $G$, and present a formula for the characteristic polynomial of the transition probability matrix of this CRW by using a
We consider a fundamental algorithmic question in spectral graph theory: Compute a spectral sparsifier of random-walk matrix-polynomial $$L_alpha(G)=D-sum_{r=1}^dalpha_rD(D^{-1}A)^r$$ where $A$ is the adjacency matrix of a weighted, undirected graph,
In this paper we consider a particular version of the random walk with restarts: random reset events which bring suddenly the system to the starting value. We analyze its relevant statistical properties like the transition probability and show how an
We experimentally study the motion of light-activated colloidal microswimmers in a viscoelastic fluid. We find that, in such a non-Newtonian environment, the active colloids undergo an unexpected transition from enhanced angular diffusion to persiste