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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Coupling by change of measures for dimension-free Harnack inequality
无维 哈纳克不等式 测度 耦合
2023/5/12
简要介绍概率论中的耦合方法及其在基础数学中的应用。引入新的变测度耦合，以简单的随机微分方程为例，将其应用于建立无穷维Harnack不等式、Bisnut导数公式和分布积分公式。
Measures of finite pluricomplex energy
Complex Monge-Ampère operator energy classes Dirichlet problem plurisubharmonic function
2011/9/1
Abstract: In this note we study a complex Monge-Amp\`{e}re type equation of the form (dd^cu)^n = \frac {ke^{-u}dV}{\int e^{-u}dV}\.
Direct spreading measures of Laguerre polynomials
Orthogonal polynomials Laguerre polynomials spreading lengths
2010/11/26
The direct spreading measures of the Laguerre polynomials L( )n (x), which quantify the distribution of its Rakhmanov probability density n, (x) = 1 d2 n x e−x h L( ) n (x)
i2 along the positi...
Typical Borel measures on $[0,1]d$ satisfy a multifractal formalism
Borel measures Hausdorff dimension Multifractal anal-ysis Baire categories
2010/11/29
In this article, we prove that in the Baire category sense, measures supported by the unit cube of Rd typically satisfy a multifractal formalism. To achieve this, we compute explicitly the multifracta...
Asymptotics of multiple orthogonal polynomials for a system of two measures supported on a starlike set
Higher-order recurrences Nikishin systems ratio asymptotics nth root asymptotics
2010/11/29
For a system of two measures supported on a starlike set in the complex plane, we study asymptotic properties of associated multiple orthogonal polynomials Qn and their recurrence coefficients. These ...
Degenerate self-similar measures, spectral asymptotics and small deviations of Gaussian processes
Degenerate self-similar measures spectral asymptotics small deviations of Gaussian processes
2010/12/1
The problem of small ball behavior for the norms of Gaussian processes is intensively studied
in recent years. The simplest and most explored case is that of L2-norm. Let us consider a
Gaussian proc...
On the parity complexity measures of Boolean functions
Computational complexity Communication complexity Parity decision tree Log-Rank conjecture
2012/11/30
The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Bool...
Interpolation of Ideal Measures by Abstract $K$ and $J$ Spaces
real interpolation ideal measures operator ideals shift operators
2007/12/10
We work with the abstract K and J interpolation method generated by a sequence lattice $\Gamma$. We investigate the deviation of an interpolated operator from a given operator ideal by establishing fo...