1-2期

最新文章

• On parabolic inequalities for generators of diffusions with jumps AI翻译
  作者：Bogachev, Vladimir I.; Roeckner, Michael; Shaposhnikov, Stanislav V.
  作者单位：Lomonosov Moscow State University; St Tikhons's University; University of Bielefeld
  摘要：We prove absolute continuity of space-time probabilities satisfying certain parabolic inequalities for generators of diffusions with jumps. As an application, we prove absolute continuity of transition probabilities of singular diffusions with jumps under minimal conditions that ensure absolute continuity of the corresponding diffusions without jumps.
• On the Gibbs states of the noncritical Potts model on Z2 AI翻译
  作者：Coquille, Loren; Duminil-Copin, Hugo; Ioffe, Dmitry; Velenik, Yvan
  作者单位：University of Geneva; Technion Israel Institute of Technology
  摘要：We prove that all Gibbs states of the -state nearest neighbor Potts model on below the critical temperature are convex combinations of the pure phases; in particular, they are all translation invariant. To achieve this goal, we consider such models in large finite boxes with arbitrary boundary condition, and prove that the center of the box lies deeply inside a pure phase with high probability. Our estimate of the finite-volume error term is of essentially optimal order, which stems from the B...
• The limiting shape for drifted internal diffusion limited aggregation is a true heat ball AI翻译
  作者：Lucas, Cyrille
  摘要：We build the iDLA cluster using drifted random walks, and study the limiting shapes they exhibit, with the help of sandpile models. For constant drift, the normalised cluster converges to a canonical shape , which can be termed a true heat ball, in that it gives rise to a mean value property for caloric functions. The existence and boundedness of such a shape answers the natural yet open question of the existence and boundedness of a shape that satisfies a mean value property for caloric funct...
• Variance asymptotics for random polytopes in smooth convex bodies AI翻译
  作者：Calka, Pierre; Yukich, J. E.
  作者单位：Universite de Rouen Normandie; Lehigh University
  摘要：Let be a smooth convex set and let be a Poisson point process on of intensity . The convex hull of is a random convex polytope . As , we show that the variance of the number of -dimensional faces of , when properly scaled, converges to a scalar multiple of the affine surface area of . Similar asymptotics hold for the variance of the number of -dimensional faces for the convex hull of a binomial process in K.