Browsing by Author "Kerimov, Azer"
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Item Open Access Ground state criteria in one-dimensional antiferromagnetic Ising model with long range interaction(American Institute of Physics Inc., 2020) Kerimov, AzerOne-dimensional long-range Ising models with antiferromagnetic, convex pair interactions are investigated. A new criterion characterizing ground states is given. The criterion and a new transformation yield short proofs identifying and characterizing the ground states. The uniqueness of periodic ground states up to shifts is shown.Item Open Access Oscillation properties of expected stopping times and stopping probabilities for patterns consisting of consecutive states in Markov chains(Rocky Mountain Mathematics Consortium, 2020) Kerimov, Azer; Öner, AbdullahWe investigate a Markov chain with a state space 1,2,…,r1,2,…,r stopping at appearance of patterns consisting of two consecutive states. It is observed that the expected stopping times of the chain have surprising oscillating dependencies on starting positions. Analogously, the stopping probabilities also have oscillating dependencies on terminal states. In a nonstopping Markov chain the frequencies of appearances of two consecutive states are found explicitly.