The Experts below are selected from a list of 153783 Experts worldwide ranked by ideXlab platform
Jiangang Ying - One of the best experts on this subject based on the ideXlab platform.
-
Effective intervals and regular Dirichlet subspaces
arXiv: Probability, 2018Co-Authors: Wenjie Sun, Jiangang YingAbstract:It is shown in [10] that a regular and local Dirichlet form on an interval can be represented by so-called effective intervals with scale functions. This paper focuses on how to operate on effective intervals to obtain regular Dirichlet subspaces. The first result is a complete characterization for a Dirichlet form to be a regular subspace of such a Dirichlet form in terms of effective intervals. Then we give an explicit road map how to obtain all regular Dirichlet subspaces from a local and regular Dirichlet form on an interval, by a series of intuitive operations on the effective intervals in the representation above. Finally applying previous results, we shall prove that every regular and local Dirichlet form has a special standard core generated by a continuous and strictly increasing function.
-
Killing Transform on Regular Dirichlet Subspaces
Potential Analysis, 2016Co-Authors: Jiangang YingAbstract:In this paper, we shall consider the killing transform induced by a multiplicative functional on regular Dirichlet subspaces of a fixed Dirichlet form. Roughly speaking, a regular Dirichlet subspace is a closed subspace with Dirichlet and regular properties of fixed Dirichlet space. By using the killing transforms, our main results indicate that the big jump part of fixed Dirichlet form is not essential for discussing its regular Dirichlet subspaces. This fact is very similar to the status of killing measure when we consider the questions about regular Dirichlet subspaces in Li-and-Ying (2015).
-
Regular subspaces of Dirichlet forms
Festschrift Masatoshi Fukushima, 2014Co-Authors: Jiangang YingAbstract:The regular subspaces of a Dirichlet form are the regular Dirichlet forms that inherit the original form but possess smaller domains. The two problems we are concerned are: (1) the existence of regular subspaces of a fixed Dirichlet form, (2) the characterization of the regular subspaces if exists. In this paper, we will first research the structure of regular subspaces for a fixed Dirichlet form. The main results indicate that the jumping and killing measures of each regular subspace are just equal to that of the original Dirichlet form. By using the independent coupling of Dirichlet forms and some celebrated probabilistic transformations, we will study the existence and characterization of the regular subspaces of local Dirichlet forms.
-
Dirichlet Forms Associated with Linear Diffusions
Chinese Annals of Mathematics Series B, 2010Co-Authors: Xing Fang, Jiangang YingAbstract:One-dimensional local Dirichlet spaces associated with linear diffusions are studied. The first result is to give a representation for any 1-dim local, irreducible and regular Dirichlet space. The second result is a necessary and sufficient condition for a Dirichlet space to be regular subspace of another Dirichlet space.
Wellingmax - One of the best experts on this subject based on the ideXlab platform.
-
Distributed Algorithms for Topic Models
Journal of Machine Learning Research, 2009Co-Authors: Newmandavid, Asuncionarthur, Smythpadhraic, WellingmaxAbstract:We describe distributed algorithms for two widely-used topic models, namely the Latent Dirichlet Allocation (LDA) model, and the Hierarchical Dirichet Process (HDP) model. In our distributed algori...
Yang Meng - One of the best experts on this subject based on the ideXlab platform.
-
Local and Non-Local Dirichlet Forms on the Sierpi\'nski Gasket and the Sierpi\'nski Carpet
2019Co-Authors: Yang MengAbstract:This thesis is about local and non-local Dirichlet forms on the Sierpi\'nski gasket and the Sierpi\'nski carpet. We are concerned with the following three problems in analysis on the Sierpi\'nski gasket and the Sierpi\'nski carpet. First, a unified purely \emph{analytic} construction of local regular Dirichlet forms on the Sierpi\'n-ski gasket and the Sierpi\'nski carpet. We give a purely analytic construction of a self-similar local regular Dirichlet form on the Sierpi\'nski carpet using $\Gamma$-convergence of stable-like non-local closed forms which gives an answer to an open problem in analysis on fractals. We also apply this construction on the Sierpi\'nski gasket. Second, determination of walk dimension \emph{without} using diffusion. Although the walk dimension is a parameter that determines the behaviour of diffusion, we give two approaches to the determination of the walk dimension \emph{prior} to the construction of diffusion. Third, approximation of local Dirichlet forms by non-local Dirichlet forms. We prove that non-local Dirichlet forms can approximate local Dirichlet forms as direct consequences of our construction of local Dirichlet forms. We also prove that on the Sierpi\'nski gasket the local Dirichlet form can be obtained as a Mosco limit of non-local Dirichlet forms. Let us emphasize that we do \emph{not} need subordination technique based on heat kernel estimates.Comment: PhD Thesis; Defended on 16 January 2019; Advisor: Prof. Alexander Grigor'yan; This thesis consists of the papers arXiv:1610.08920, arXiv:1612.05015, arXiv:1706.03318 and arXiv:1706.0499
Jeffrey Hoffstein - One of the best experts on this subject based on the ideXlab platform.
-
weyl group multiple Dirichlet series iii eisenstein series and twisted unstable ar
Annals of Mathematics, 2007Co-Authors: Benjamin Brubaker, Daniel Bump, Solomon Friedberg, Jeffrey HoffsteinAbstract:Weyl group multiple Dirichlet series were associated with a root system and a number field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hostein [3] and Brubaker, Bump and Friedberg [4] provided n is suciently large; their coecients involve n-th order Gauss sums. The case where n is small is harder, and is addressed in this paper when = Ar. “Twisted” Dirichet series are considered, which contain the series of [4] as a special case. These series are not Euler products, but due to the twisted multiplicativity of their coecients, they are determined by their p-parts. The p-part is given as a sum of products of Gauss sums, parametrized by strict Gelfand-Tsetlin patterns. It is conjectured that these multiple Dirichlet series are Whittaker coecients of Eisenstein series on the n-fold metaplectic cover of GLr+1, and this is proved if r = 2 or n = 1. The equivalence of our definition with that of Chinta [11] when n = 2 and r 6 5 is also established.
Shui Feng - One of the best experts on this subject based on the ideXlab platform.
-
the poisson Dirichlet distribution and related topics models and asymptotic behaviors
2010Co-Authors: Shui FengAbstract:Models.- The Poisson-Dirichlet Distribution.- The Two-Parameter Poisson-Dirichlet Distribution.- The Coalescent.- Stochastic Dynamics.- Particle Representation.- Asymptotic Behaviors.- Fluctuation Theorems.- Large Deviations for the Poisson-Dirichlet Distribution.- Large Deviations for the Dirichlet Processes.
-
Some Diffusion Processes Associated With Two Parameter Poisson-Dirichlet Distribution and Dirichlet Process
Probability Theory and Related Fields, 2009Co-Authors: Shui Feng, Wei SunAbstract:The two parameter Poisson–Dirichlet distribution PD(α, θ) is the distribution of an infinite dimensional random discrete probability. It is a generalization of Kingman’s Poisson–Dirichlet distribution. The two parameter Dirichlet process \({\Pi_{\alpha,\theta,\nu_0}}\) is the law of a pure atomic random measure with masses following the two parameter Poisson–Dirichlet distribution. In this article we focus on the construction and the properties of the infinite dimensional symmetric diffusion processes with respective symmetric measures PD(α, θ) and \({\Pi_{\alpha,\theta,\nu_0}}\). The methods used come from the theory of Dirichlet forms.
-
Some Diffusion Processes Associated With Two Parameter Poisson-Dirichlet Distribution and Dirichlet Process
arXiv: Probability, 2009Co-Authors: Shui Feng, Wei SunAbstract:The two parameter Poisson-Dirichlet distribution $PD(\alpha,\theta)$ is the distribution of an infinite dimensional random discrete probability. It is a generalization of Kingman's Poisson-Dirichlet distribution. The two parameter Dirichlet process $\Pi_{\alpha,\theta,\nu_0}$ is the law of a pure atomic random measure with masses following the two parameter Poisson-Dirichlet distribution. In this article we focus on the construction and the properties of the infinite dimensional symmetric diffusion processes with respective symmetric measures $PD(\alpha,\theta)$ and $\Pi_{\alpha,\theta,\nu_0}$. The methods used come from the theory of Dirichlet forms.
-
Large Deviations for Dirichlet Processes and Poisson-Dirichlet Distribution with Two Parameters
Electronic Journal of Probability, 2007Co-Authors: Shui FengAbstract:Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter $\theta$ approaches infinity. The motivation for these results is to understand the differences in terms of large deviations between the two-parameter models and their one-parameter counterparts. New insight is obtained about the role of the second parameter $\alpha$ through a comparison with the corresponding results for the one-parameter Poisson-Dirichlet distribution and Dirichlet process.
