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作者：Diaconis, Persi; Houston-Edwards, Kelsey; Saloff-Coste, Laurent
作者单位：Stanford University; Franklin W. Olin College of Engineering; Cornell University
摘要：Gambler's ruin estimates can be viewed as harmonic measure estimates for finite Markov chains which are absorbed (or killed) at boundary points. We relate such estimates to properties of the underlying chain and its Doob transform. Precisely, we show that gambler's ruin estimates reduce to a good understanding of the Perron-Frobenius eigenfunction and eigenvalue whenever the underlying chain and its Doob transform are Harnack Markov chains. Finite inner-uniform domains (say, in the square grid...
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作者：Gan, Han L.; Ross, Nathan
作者单位：Northwestern University; University of Melbourne
摘要：We provide a general theorem bounding the error in the approximation of a random measure of interest-for example, the empirical population measure of types in a Wright-Fisher model-and a Dirichlet process, which is a measure having Poisson-Dirichlet distributed atoms with i.i.d. labels from a diffuse distribution. The implicit metric of the approximation theorem captures the sizes and locations of the masses, and so also yields bounds on the approximation between the masses of the measure of i...
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作者：Chleboun, Paul; Smith, Aaron
作者单位：University of Warwick; University of Ottawa
摘要：Plaquette models are short range ferromagnetic spin models that play a key role in the dynamic facilitation approach to the liquid glass transition. In this paper we study the dynamics of the square plaquette model at the smallest of the three critical length scales discovered in ( J. Stat. Phys. 169 (2017) 441-471). Our main result is that the plaquette model with periodic boundary conditions, on this length scale, exhibits a sharp transition in the convergence to equilibrium, known as cutoff...
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作者：Hofmanova, Martina; Leahy, James-Michael; Nilssen, Torstein
作者单位：University of Bielefeld; Imperial College London; University of Agder
摘要：We introduce a rough perturbation of the Navier-Stokes system and justify its physical relevance from balance of momentum and conservation of circulation in the inviscid limit. We present a framework for a well-posedness analysis of the system. In particular, we define an intrinsic notion of strong solution based on ideas from the rough path theory and study the system in an equivalent vorticity formulation. In two space dimensions, we prove that well-posedness and enstrophy balance holds. Mor...
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作者：Wang, Andi Q.; Pollock, Murray; Roberts, Gareth O.; Steinsaltz, David
作者单位：University of Bristol; Newcastle University - UK; University of Warwick; University of Oxford
摘要：We study a class of Markov processes that combine local dynamics, arising from a fixed Markov process, with regenerations arising at a state-dependent rate. We give conditions under which such processes possess a given target distribution as their invariant measures, thus making them amenable for use within Monte Carlo methodologies. Since the regeneration mechanism can compensate the choice of local dynamics, while retaining the same invariant distribution, great flexibility can be achieved i...
