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作者：Pfaffelhuber, P.; Wakolbinger, A.; Weisshaupt, H.
作者单位：University of Freiburg; Goethe University Frankfurt; University of Freiburg
摘要：A well-established model for the genealogy of a large population in equilibrium is Kingman's coalescent. For the population together with its genealogy evolving in time, this gives rise to a time-stationary tree-valued process. We study the sum of the branch lengths, briefly denoted as tree length, and prove that the (suitably compensated) sequence of tree length processes converges, as the population size tends to infinity, to a limit process with cA dlA g paths, infinite infinitesimal varian...
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作者：Barlow, Martin T.; Cerny, Jiri
作者单位：University of British Columbia; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider a random walk among unbounded random conductances whose distribution has infinite expectation and polynomial tail. We prove that the scaling limit of this process is a Fractional-Kinetics process-that is the time change of a d-dimensional Brownian motion by the inverse of an independent alpha-stable subordinator. We further show that the same process appears in the scaling limit of the non-symmetric Bouchaud's trap model.
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作者：Morris, Robert
作者单位：University of Cambridge
摘要：We study zero-temperature Glauber dynamics on Z(d), which is a dynamic version of the Ising model of ferromagnetism. Spins are initially chosen according to a Bernoulli distribution with density p, and then the states are continuously (and randomly) updated according to the majority rule. This corresponds to the sudden quenching of a ferromagnetic system at high temperature with an external field, to one at zero temperature with no external field. Define p(c) (Z(d)) to be the infimum over p su...
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作者：Cerf, R.; Messikh, R. J.
作者单位：Universite Paris Saclay; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We study the 2D-Ising model defined on finite boxes at temperatures that are below but very close from the critical point. When the temperature approaches the critical point and the size of the box grows fast enough, we establish large deviations estimates on FK-percolation events that concern the phenomenon of phase coexistence.
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作者：Damron, Michael; Sapozhnikov, Artem
作者单位：Princeton University
摘要：We study invasion percolation in two dimensions, focusing on properties of the outlets of the invasion and their relation to critical percolation and to incipient infinite clusters (IICs). First we compute the exact decay rate of the distribution of both the weight of the kth outlet and the volume of the kth pond. Next we prove bounds for all moments of the distribution of the number of outlets in an annulus. This result leads to almost sure bounds for the number of outlets in a box B(2 (n) ) ...
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作者：Mirek, Mariusz
作者单位：University of Wroclaw
摘要：We consider the Markov chain {X-n(x)}(n=0)(infinity) = 0 on R-d defined by the stochastic recursion X-n(x) = psi(theta n) (X-n-1(x)), starting at x is an element of R-d, where theta(1), theta(2), ... are i.i.d. random variables taking their values in a metric space (Theta, r), and psi(theta n) : R-d -> R-d are Lipschitz maps. Assume that theMarkov chain has a unique stationary measure.. Under appropriate assumptions on psi(theta n) , we will show that the measure. has a heavy tail with the exp...
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作者：Banica, Teodor; Curran, Stephen; Speicher, Roland
作者单位：CY Cergy Paris Universite; University of California System; University of California Berkeley; Queens University - Canada
摘要：We consider several orthogonal quantum groups satisfying the easiness assumption axiomatized in our previous paper. For each of them we discuss the computation of the asymptotic law of Tr(u (k) ) with respect to the Haar measure, u being the fundamental representation. For the classical groups O (n) , S (n) we recover in this way some well-known results of Diaconis and Shahshahani.
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作者：Chen, Xin; Li, Xue-Mei; Wu, Bo
作者单位：University of Warwick; University of Warwick
摘要：The aim of the paper is to study the pinned Wiener measure on the loop space over a simply connected compact Riemannian manifold together with a Hilbert space structure and the Ornstein-Uhlenbeck operator d*d. We give a concrete estimate for the weak Poincar, inequality, assuming positivity of the Ricci curvature of the underlying manifold. The order of the rate function is s (-alpha) for any alpha > 0.
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作者：Li, Xiang-Dong
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Fudan University; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Based on a new martingale representation formula, we prove some quantitative upper bound estimates of the L (p) -norm of some singular integral operators on complete Riemannian manifolds. This leads us to establish the Weak L (p) -Hodge decomposition theorem and to prove the L (p) -boundedness of the Beurling-Ahlfors transforms on complete non-compact Riemannian manifolds with non-negative Weitzenbock curvature operator.
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作者：Daskalakis, Constantinos; Mossel, Elchanan; Roch, Sebastien
作者单位：University of California System; University of California Los Angeles; Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley; Weizmann Institute of Science
摘要：A major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on a tree. Given samples from the leaves of the Markov chain, the goal is to reconstruct the leaf-labelled tree. It is well known that in order to reconstruct a tree on n leaves, sample sequences of length Omega (log n) are needed. It was conjectured by Steel that for the CFN/Ising evolutionary model, if the mutation probability on all edges of...
