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作者：Cheek, David; Antal, Tibor
作者单位：University of Edinburgh
摘要：First, we revisit the stochastic Luria-Delbruck model: a classic two-type branching process which describes cell proliferation and mutation. We prove limit theorems and exact results for the mutation times, clone sizes and number of mutants. Second, we extend the framework to consider mutations at multiple sites along the genome. The number of mutants in the two-type model characterises the mean site frequency spectrum in the multiple-site model. Our predictions are consistent with previously ...
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作者：Shneer, Seva; Stolyar, Alexander
作者单位：Heriot Watt University; University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We consider a stochastic queueing system modelling the behaviour of a wireless network with nodes employing a discrete-time version of the standard decentralised medium access algorithm. The system is unsaturated-ach node receives an exogenous flow of packets at the rate of. packets per time slot. Each packet takes one slot to transmit, but neighbouring nodes cannot transmit simultaneously. The algorithm we study is standard in the following sense: a node with an empty queue does not compete f...
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作者：Bally, Vlad; Goreac, Dan; Rabiet, Victor
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Universite Gustave-Eiffel
摘要：We consider stochastic differential systems driven by a Brownian motion and a Poisson point measure where the intensity measure of jumps depends on the solution. This behavior is natural for several physical models (such as Boltzmann equation, piecewise deterministic Markov processes, etc.). First, we give sufficient conditions guaranteeing that the semigroup associated with such an equation preserves regularity by mapping the space of k-times differentiable bounded functions into itself. Furt...
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作者：Bjornberg, Jakob E.; Ueltschi, Daniel
作者单位：Chalmers University of Technology; University of Gothenburg; University of Warwick
摘要：We give estimates of the critical parameter for random loop models that are related to quantum spin systems. A special case of the model that we consider is the interchange- or random-stirring process. We consider here the model defined on regular trees of large degrees, which are expected to approximate high spatial dimensions. We find a critical parameter that indeed shares similarity with existing numerical results for the cubic lattice. In the case of the interchange process, our results i...
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作者：Deligiannidis, George; Lee, Anthony
作者单位：University of Oxford; University of Warwick; University of Bristol; Alan Turing Institute
摘要：We show that the class of L-2 functions for which ergodic averages of a reversible Markov chain have finite asymptotic variance is determined by the class of L-2 functions for which ergodic averages of its associated jump chain have finite asymptotic variance. This allows us to characterize completely which ergodic averages have finite asymptotic variance when the Markov chain is an independence sampler. From a practical perspective, the most important result identifies a simple sufficient con...
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作者：Turova, Tatyana S.
作者单位：Lund University
摘要：We consider the system of particles on a finite interval with pairwise nearest neighbours interaction and external force. This model was introduced by Malyshev [Probl. Inf. Transm. 51 (2015) 31-36] to study the flow of charged particles on a rigorous mathematical level. It is a simplified version of a 3-dimensional classical Coulomb gas model. We study Gibbs distribution at finite positive temperature extending recent results on the zero temperature case (ground states). We derive the asymptot...
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作者：Alt, Johannes; Erdos, Laszlo; Krueger, Torben
作者单位：Institute of Science & Technology - Austria
摘要：We consider large random matrices X with centered, independent entries, which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical variances, the limiting density is uniform. In this special case, the local circular law by Bourgade et al. [Probab. Theory Related Fields 159 (2014) 545-595; Probab. Theory Related Fields 159 (2014) 619-660] shows that the empirical density converges even locally on ...
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作者：De Angelis, Tiziano; Ferrari, Giorgio; Moriarty, John
作者单位：University of Leeds; University of Bielefeld; University of London; Queen Mary University London
摘要：This paper analyses two-player nonzero-sum games of optimal stopping on a class of linear regular diffusions with not nonsingular boundary behaviour [in the sense of Ito and McKean (Diffusion Processes and Their Sample Paths (1974) Springer, page 108)]. We provide sufficient conditions under which Nash equilibria are realised by each player stopping the diffusion at one of the two boundary points of an interval. The boundaries of this interval solve a system of algebraic equations. We also pro...
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作者：Dombry, Clement; Hashorva, Enkelejd; Soulier, Philippe
作者单位：Universite Marie et Louis Pasteur; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Lausanne
摘要：The goal of this paper is an exhaustive investigation of the link between the tail measure of a regularly varying time series and its spectral tail process, independently introduced in [Owada and Samorodnitsky (2012)] and [Stochastic Process. Appl. 119 (2009) 1055-1080]. Our main result is to prove in an abstract framework that there is a one-to-one correspondence between these two objects, and given one of them to show that it is always possible to build a time series of which it will be the ...
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作者：Reygner, Julien
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Gustave-Eiffel
摘要：We consider particle systems with mean-field interactions whose distribution is invariant by translations. Under the assumption that the system seen from its centre of mass be reversible with respect to a Gibbs measure, we establish large deviation principles for its empirical measure at equilibrium. Our study covers the cases of McKean-Vlasov particle systems without external potential, and systems of rank-based interacting diffusions. Depending on the strength of the interaction, the large d...
