for an m-state homogeneous irreducible Markov chain with transition probability matrix Qm×m is known, but the chain requires updating by altering some of its transition probabilities or by adding or deleting some states. Suppose that the updated transition probability matrix Pn×n is also irreducible. The updating problem is to compute the updated stationary distribution π = (π1, π2, . . . , πn)...

We study the nature of the phase transition in the multifractal formalism of the harmonic measure of diffusion limited aggregates. Contrary to previous work that relied on random walk simulations or ad hoc models to estimate the low probability events of deep fjord penetration, we employ the method of iterated conformal maps to obtain an accurate computation of the probability of the rarest eve...

We present an alternative approach to the problem of interacting fluids, which we believe may provide important insights into microscopic mechanisms that lead to the occurrence of phase transitions. The approach exploits enumerative properties and combinatorial meaning of Bell polynomials. We derive the exact formula for the probability of a general system of N particles at temperature T to con...

In this paper we develop a new model and propose an iterative method to calculate stationary probability vector of a transition probability tensor arising from a higher-order Markov chain. Existence and uniqueness of such stationary probability vector are studied. We also discuss and compare the results of the new model with those by the eigenvector method for a nonnegative tensor. Numerical ex...

In this paper we consider a null recurrent random walk in random environment on a super-critical Galton-Watson tree. We consider the case where the log-Laplace transform ψ of the branching process satisfies ψ(1) = ψ′(1) = 0 for which G. Faraud, Y. Hu and Z. Shi have shown that, with probability one, the largest generation visited by the walk, until the instant n, is of the order of (logn). We h...

We present a formalism to calculate the probability distribution function of a scalar field coarse-grained over some spatial scales with a Gaussian filter at finite temperature. As an application, we investigate the role of subcritical fluctuations in the electroweak phase transition in the minimal standard model. It is concluded that the universe was in a mixed state of true and false vacua al...

The probability of an event's occurrence affects event-related potentials (ERPs) on electroencephalograms. The relation between probability and potentials has been discussed by using a quantity called surprise that represents the self-information that humans receive from the event. Previous studies have estimated surprise based on the probability distribution in a stationary state. Our hypothes...

A categorical approach to probability allows to put basic notions of probability into a broader mathematical perspective, to evaluate their roles, and mutual relationships. Classical probability theory and fuzzy probability theory lead to two particular categories and their relationship (in categorical terms) enable us to understand and explicitly formulate the difference between them. Using ou...