Probability Theory and Related Fields

最新文章

• High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations AI翻译
  作者：Flandoli, Franco; Luo, Dejun
  作者单位：Scuola Normale Superiore di Pisa; Chinese Academy of Sciences; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
  摘要：The paper is concerned with the problem of regularization by noise of 3D Navier-Stokes equations. As opposed to several attempts made with additive noise which remained inconclusive, we show here that a suitable multiplicative noise of transport type has a regularizing effect. It is proven that stochastic transport noise provides a bound on vorticity which gives well posedness, with high probability. The result holds for sufficiently large noise intensity and sufficiently high spectrum of the ...
• Power-law bounds for critical long-range percolation below the upper-critical dimension AI翻译
  作者：Hutchcroft, Tom
  作者单位：University of Cambridge
  摘要：We study long-range Bernoulli percolation on Z(d) in which each two vertices x and y are connected by an edge with probability 1 - exp(-beta parallel to x - y parallel to(-d-alpha)). It is a theorem of Noam Berger (Commun. Math. Phys., 2002) that if 0 < alpha < d then there is no infinite cluster at the critical parameter beta(c). We give a new, quantitative proof of this theorem establishing the power-law upper bound P-beta c (vertical bar K vertical bar >= n) <= Cn(-(d-alpha)/(2d+alpha)) for...
• Quantum SL2, infinite curvature and Pitman's 2M-X theorem AI翻译
  作者：Chapon, Francois; Chhaibi, Reda
  作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
  摘要：The classical theorem by Pitman states that a Brownianmotionminus twice its running infimum enjoys the Markov property. On the one hand, Biane understood that Pitman's theorem is intimately related to the representation theory of the quantum group U-q (sl(2)), in the so-called crystal regime q -> 0. On the other hand, Bougerol and Jeulin showed the appearance of exactly the same Pitman transform in the infinite curvature limit r. 8 of a Brownian motion on the hyperbolic space H-3 = SL2(C)/SU2....
• On the maximal displacement of near-critical branching random walks AI翻译
  作者：Neuman, Eyal; Zheng, Xinghua
  作者单位：Imperial College London; Hong Kong University of Science & Technology
  摘要：We consider a branching random walk on Z started by n particles at the origin, where each particle disperses according to a mean-zero random walk with bounded support and reproduces with mean number of offspring 1 + theta/n. For t >= 0, we study M-nt, the rightmost position reached by the branching random walk up to generation [nt]. Under certain moment assumptions on the branching law, we prove that M-nt/root n converges weakly to the rightmost support point of the local time of the limiting ...
• Phase transitions for a class of gradient fields AI翻译
  作者：Buchholz, Simon
  作者单位：University of Bonn
  摘要：We consider gradient fields on Z(d) for potentials V that can be expressed as e(-V(x)) = pe -qx(2)/2 + (1 - p)e-x(2)/2. This representation allows us to associate a random conductance type model to the gradient fields with zero tilt. We investigate this random conductance model and prove correlation inequalities, duality properties, and uniqueness of the Gibbs measure in certain regimes. We then show that there is a close relation between Gibbs measures of the random conductance model and grad...
• Editorial AI翻译
  作者：[Anonymous]
• Interacting diffusions on positive definite matrices AI翻译
  作者：O'Connell, Neil
  作者单位：University College Dublin
  摘要：We consider systems of Brownian particles in the space of positive definite matrices, which evolve independently apart from some simple interactions. We give examples of such processes which have an integrable structure. These are related to K-Bessel functions of matrix argument and multivariate generalisations of these functions. The latter are eigenfunctions of a particular quantisation of the non-Abelian Toda lattice.
• The diameter of uniform spanning trees in high dimensions AI翻译
  作者：Michaeli, Peleg; Nachmias, Asaf; Shalev, Matan
  作者单位：Tel Aviv University
  摘要：We show that the diameter of a uniformly drawn spanning tree of a connected graph on n vertices which satisfies certain high-dimensionality conditions typically grows like Theta(root n). In particular this result applies to expanders, finite tori Z(m)(d) of dimension d >= 5, the hypercube {0, 1}(m), and small perturbations thereof.
• The distance exponent for Liouville first passage percolation is positive AI翻译
  作者：Ding, Jian; Gwynne, Ewain; Sepulveda, Avelio
  作者单位：University of Pennsylvania; University of Chicago; Universidad de Chile
  摘要：Discrete Liouville first passage percolation (LFPP) with parameter xi > 0 is the random metric on a sub-graph of Z(2) obtained by assigning each vertex z a weight of e(xi h(z)), where h is the discrete Gaussian free field. We show that the distance exponent for discrete LFPP is strictly positive for all xi > 0. More precisely, the discrete LFPP distance between the inner and outer boundaries of a discrete annulus of size 2(n) is typically at least 2(alpha n) for an exponent alpha > 0 depending...
• A free boundary characterisation of the Root barrier for Markov processes AI翻译
  作者：Gassiat, Paul; Oberhauser, Harald; Zou, Christina Z.
  作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Oxford
  摘要：We study the existence, optimality, and construction of non-randomised stopping times that solve the Skorokhod embedding problem (SEP) for Markov processes which satisfy a duality assumption. These stopping times are hitting times of space-time subsets, so-called Root barriers. Our main result is, besides the existence and optimality, a potential-theoretic characterisation of this Root barrier as a free boundary. If the generator of the Markov process is sufficiently regular, this reduces to a...