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作者：Tetali, Prasad; Vera, Juan C.; Vigoda, Eric; Yang, Linji
作者单位：University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology; Tilburg University
摘要：We prove that the mixing time of the Glauber dynamics for random k-colorings of the complete tree with branching factor b undergoes a phase transition at k = b(1 + o(b)(1))/In b. Our main result shows nearly sharp bounds on the mixing time of the dynamics on the complete tree with n vertices for k = Cb/In b colors with constant C. For C >= 1 we prove the mixing time is O(n(1+ob(1)) In n). On the other side, for C < 1 the mixing time experiences a slowing down; in particular, we prove it is O(n...
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作者：Bodineau, Thierry; Lagouge, Maxime
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite
摘要：We derive a large deviation principle for the empirical currents of lattice gas dynamics which combine a fast stirring mechanism (Symmetric Simple Exclusion Process) and creation/annihilation mechanisms (Glauber dynamics). Previous results on the density large deviations can be recovered from this general large deviation principle. The contribution of external driving forces due to reservoirs at the boundary of the system is also taken into account.
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作者：Decrouez, Geoffrey; Jones, Owen Dafydd
作者单位：University of Melbourne
摘要：We present a new class of multifractal process on R, constructed using an embedded branching process. The construction makes use of known results on multitype branching random walks, and along the way constructs cascade measures on the boundaries of multitype Galton-Watson trees. Our class of processes includes Brownian motion subjected to a continuous multifractal time-change. In addition, if we observe our process at a fixed spatial resolution, then we can obtain a finite Markov representati...
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作者：Bender, Christian
作者单位：Saarland University
摘要：We characterize absence of arbitrage with simple trading strategies in a discounted market with a constant bond and several risky assets. We show that if there is a simple arbitrage, then there is a 0-admissible one or an obvious one, that is, a simple arbitrage which promises a minimal riskless gain of E, if the investor trades at all. For continuous stock models, we provide an equivalent condition for absence of 0-admissible simple arbitrage in terms of a property of the fine structure of th...
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作者：Griffin, Philip S.; Maller, Ross A.
作者单位：Syracuse University; Australian National University; Australian National University
摘要：We analyze the general Levy insurance risk process for Levy measures in the convolution equivalence class S-(alpha), alpha > 0, via a new kind of path decomposition. This yields a very general functional limit theorem as the initial reserve level u -> infinity, and a host of new results for functionals of interest in insurance risk. Particular emphasis is placed on the time to ruin, which is shown to have a proper limiting distribution, as u > infinity, conditional on ruin occurring under our ...
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作者：Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E.
作者单位：University of Munich; Princeton University; Goethe University Frankfurt
摘要：On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient. On the other hand, the implicit Euler scheme is known to converge strongly to the exact solution of such an SDE. Implementations of the implicit Euler scheme, however, require additional computational effort. In this article we therefore propose an explicit and easily i...
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作者：Litterer, C.; Lyons, T.
作者单位：Imperial College London; University of Oxford; University of Oxford
摘要：Particle methods are widely used because they can provide accurate descriptions of evolving measures. Recently it has become clear that by stepping outside the Monte Carlo paradigm these methods can be of higher order with effective and transparent error bounds. A weakness of particle methods (particularly in the higher order case) is the tendency for the number of particles to explode if the process is iterated and accuracy preserved. In this paper we identify a new approach that allows dynam...
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作者：Etheridge, A. M.; Veber, A.
作者单位：University of Oxford; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We extend the spatial A-Fleming-Viot process introduced in [Electron. J. Probab. 15 (2010) 162-216] to incorporate recombination. The process models allele frequencies in a population which is distributed over the two-dimensional torus T(L) of sideleneth L and is subject to two kinds of reproduction events: small events of radius O(1) and much rarer large events of radius O(L-alpha) for some alpha is an element of (0, 1]. We investigate the correlation between the times to the most recent comm...
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作者：Houdre, Christian; Talata, Zsolt
作者单位：University System of Georgia; Georgia Institute of Technology; University of Kansas
摘要：The rate of convergence of the distribution of the length of the longest increasing subsequence, toward the maximal eigenvalue of certain matrix ensembles, is investigated. For finite-alphabet uniform and nonuniform i.i.d. sources, a rate of log n/root n is obtained. The uniform binary case is further explored, and an improved 1/root n rate obtained.
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作者：Martinelli, Fabio; Sinclair, Alistair
作者单位：Roma Tre University; University of California System; University of California Berkeley
摘要：We analyze the mixing time of a natural local Markov chain (the Glauber dynamics) on configurations of the solid-on-solid model of statistical physics. This model has been proposed, among other things, as an idealization of the behavior of contours in the Ising model at low temperatures. Our main result is an upper bound on the mixing time of (O) over tilde (n(3.5)), which is tight within a factor of (O) over tilde(root n). The proof, which in addition gives some insight into the actual evolut...
