1,143 research outputs found
Convergence of Non-Symmetric Diffusion Processes on RCD spaces
We construct non-symmetric diffusion processes associated with Dirichlet
forms consisting of uniformly elliptic forms and derivation operators with
killing terms on RCD spaces by aid of non-smooth differential structures
introduced by Gigli '16. After constructing diffusions, we investigate
conservativeness and the weak convergence of the laws of diffusions in terms of
a geometric convergence of the underling spaces and convergences of the
corresponding coefficients.Comment: 41 pages. To appear in Calc. Var. PDEs. In the second version, the
following have been modified: Section 2.3, 2.4, 2.5, 2.6 were added.
Assumption 3.3, Proposition 3.4, Remark 3.5, and Example 3.7 were deleted.
Example 7.2 was replaced with Corollary 7.2. Theorem 4.4 was modifie
Convergence of Brownian Motions on Metric Measure Spaces Under Riemannian Curvature-Dimension Conditions
We show that the pointed measured Gromov convergence of the underlying spaces
implies (or under some condition, is equivalent to) the weak convergence of
Brownian motions under Riemannian Curvature-Dimension (RCD) conditions.Comment: 39 pages, 3 figures. Final version. To appear in EJP. Theorem 1.4 has
been modified with the time interval [\epsilon, \infty
Convergences and projection Markov property of Markov processes on ultrametric spaces
Let be an ultrametric space with certain conditions and be
the quotient space of with respect to the partition by balls with a fixed
radius . We prove that, for a Hunt process on associated with
a Dirichlet form , a Hunt process on
associated with the averaged Dirichlet form is
Mosco convergent to , and under certain additional conditions,
converges weakly to . Moreover, we give a sufficient condition for the
Markov property of to be preserved under the canonical projection
to . In this case, we see that the projected process is
identical in law to and converges weakly to .Comment: 17 page
On the ergodicity of interacting particle systems under number rigidity
In this paper, we provide relations among the following properties:(a) the tail triviality of a probability measure μ on the configuration space ϒ; (b) the finiteness of a suitable L2-transportation-type distance d¯ϒ; (c) the irreducibility of local μ-symmetric Dirichlet forms on ϒ. As an application, we obtain the ergodicity (i.e., the convergence to the equilibrium) of interacting infinite diffusions having logarithmic interaction and arising from determinantal/permanental point processes including sine2, Airy2, Besselα,2 (α ≥ 1), and Ginibre point processes. In particular, the case of the unlabelled Dyson Brownianmotion is covered. For the proof, the number rigidity of point processes in the sense of Ghosh–Peres plays a key role
An Algorithmic Framework for Computing Validation Performance Bounds by Using Suboptimal Models
Practical model building processes are often time-consuming because many
different models must be trained and validated. In this paper, we introduce a
novel algorithm that can be used for computing the lower and the upper bounds
of model validation errors without actually training the model itself. A key
idea behind our algorithm is using a side information available from a
suboptimal model. If a reasonably good suboptimal model is available, our
algorithm can compute lower and upper bounds of many useful quantities for
making inferences on the unknown target model. We demonstrate the advantage of
our algorithm in the context of model selection for regularized learning
problems
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