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作者：Chlebicka, Iwona; Latuszynski, Krzysztof; Miasojedow, Blaej
作者单位：University of Warsaw; University of Warwick
摘要：Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used in computational physics and statistical computing. Yet, their most fun- damental properties, such as relations between convergence characteristics of their various versions, are not well understood. In this paper we prove the solidarity principle of the spectral gap for the Gibbs sampler: if any of the random scan or d! deterministic scans has a spec- tral gap then all of them have. Our methods rely on geometric interpreta...
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作者：Casanova, ADRIaN GONZaLEZ; Spano, Dario; Wilke-berenguer, Maite
作者单位：Arizona State University; Arizona State University-Tempe; University of Warwick; Humboldt University of Berlin
摘要：We analyse a family of two-types Wright-Fisher models with selection in a random environment and skewed offspring distribution. We provide a calculable criterion to quantify the impact of different shapes of selection on the fate of the weakest allele, and thus compare them. The main mathematical tool is duality, which we prove to hold, also in presence of random environment (quenched and in some cases annealed), between the population's allele frequencies and genealogy, both in the case of fi...
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作者：Agresti, Antonio; Hieber, Matthias; Hussein, Amru; Saal, Martin
作者单位：Institute of Science & Technology - Austria; Technical University of Darmstadt; University of Kaiserslautern
摘要：In this paper, we introduce and study the primitive equations with non- isothermal turbulent pressure and transport noise. They are derived from the Navier-Stokes equations by employing stochastic versions of the Boussinesq and the hydrostatic approximations. The temperature dependence of the turbulent pressure can be seen as a consequence of an additive noise acting on the small vertical dynamics. For such a model we prove global well-posedness in H1 where the noise is considered in both the ...
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作者：Forsstrom, Malin p.; Lenells, Jonatan; Viklund, Fredrik
作者单位：Chalmers University of Technology; Royal Institute of Technology
摘要：We consider the 4D fixed length lattice Higgs model with Wilson action for the gauge field and structure group Zn. We study Wilson line observables in the strong coupling regime and compute their asymptotic behavior with error estimates. Our analysis is based on a high-temperature representation of the lattice Higgs measure combined with Poisson approximation. We also give a short proof of the folklore result that Wilson line (and loop) expectations exhibit perimeter law decay whenever the Hig...
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作者：Pedrotti, Francesco
作者单位：Institute of Science & Technology - Austria
摘要：Contractive coupling rates have been recently introduced by Conforti as a and Poincar & eacute; inequality) for some classes of Markov chains. In this work, for most of the examples discussed by Conforti, we use contractive coupling rates to prove stronger inequalities, in the form of curvature lower bounds (in entropic and discrete Bakry-& Eacute;mery sense) and geodesic convexity of some entropic functionals. In addition, we recall and give straightforward generalizations of some notions of ...
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作者：Schweinsberg, Jason; Shuai, Yubo
作者单位：University of California System; University of California San Diego
摘要：Consider a birth and death process started from one individual in which each individual gives birth at rate lambda and dies at rate mu, so that the population size grows at rater = lambda - mu. Lambert (Theor. Popul. Biol. 122 (2018) 30-35) and Harris, Johnston, and Roberts (Ann. Appl. Probab. 30 (2020) 1368-1414) came up with methods for constructing the exact genealogy of a sample of size n taken from this population at time T. We use the construction of Lambert, which is based on the coales...
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作者：Friz, Peter k.; Salkeld, William; Wagenhofer, Thomas
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Nottingham; Technical University of Berlin
摘要：We consider a class of stochastic processes with rough stochastic volatility, examples of which include the rough Bergomi and rough Stein-Stein model, that have gained considerable importance in quantitative finance. A basic question for such (non-Markovian) models concerns efficient numerical schemes. While strong rates are well understood (order H), we tackle here the intricate question of weak rates. Our main result asserts that the weak rate, for a reasonably large class of test function, ...
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作者：Chen, Chenyang; Ge, Hao
作者单位：Peking University
摘要：We consider a stochastic interacting vortex system of N particles, approximating the vorticity formulation of the 2-D Navier-Stokes equation on a torus. The singular interaction kernel is given by the Biot-Savart law. Assuming only that the initial state has finite energy, we derive a sample-path large deviation principle for the empirical measure as the number of vortices tends to infinity. This contrasts with previous studies that require the initial state to have finite entropy. The rate fu...
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作者：Mossel, Elchanan; Niles-Weed, Jonathan; Sohn, Youngtak; Sun, Nike; Zadik, Ilias
作者单位：Massachusetts Institute of Technology (MIT); New York University; New York University
摘要：We connect the study of phase transitions in high-dimensional statistical inference to the study of threshold phenomena in random graphs. A major question in the study of the Erdos-R & eacute;nyi random graph G(n, p) is to understand the probability, as a function of p p, that G(n, p) contains a given subgraph H = H Hn Hn. This was studied for many specific examples of H H, starting with classical work of Erdos and R & eacute;nyi (1960). More recent work studies this question for general H H, ...
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作者：Cordero, Fernando; Hummel, Sebastian; Vechambre, Gregoire
作者单位：University of Bielefeld; University of California System; University of California Berkeley; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：Our results characterize the long-term behavior for a broad class of ronmental selection. In particular, we reveal a rich variety of parameterdependent behaviors and provide explicit criteria to discriminate between them. That includes the situation in which both boundary points, 0 and 1, are repelling-a new phenomenon in this context. This has significant biological implications, because it means that selection alone can maintain genetic variation, that is, coexistence. If a boundary point is...
