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Qingyang Guan

Publications and source records attributed to Qingyang Guan.

5 recordsLinked to original sources
arXiv2025

On tail probability of the covariance matrix in Eldan's stochastic localization

The Eldan's stochastic localization is a new kind of stochastic evolution in the space of probability measures which provides a novel way to study high dimensional convex body. A central object in the study of the stochastic localization is the stochastic process of its covariance matrix. The main result of this paper is some exponential-type tail probability estimate of the covariance process for the general time. This estimate implies a weaker version of a $p$-moment conjecture by Klartag and Lehec. The stochastic localization considered here is a simplified version by Lee and Vemplala.

math.PR↗
arXiv2024

A note on Bourgain's slicing problem

This note is to study Bourgain's slicing problem following the routes investigated in the last decade. We show that the slicing constant $L_n$ is bounded by $C\log(\log n) $, $n\geq 3$, for some universal constant $C$.

math.MG↗
arXiv2009

Boundary Harnack inequalities for regional fractional Laplacian

We consider boundary Harnack inequalities for regional fractional Laplacian which are generators of censored stable-like processes on G taking κ(x,y)/|x-y|^{n+α}dxdy, x,y\in G as the jumping measure. When G is a C^{1,β-1} open set, 1<α<β\leq 2 and κ\in C^{1}(\overline{G}\times \overline{G}) bounded between two positive numbers, we prove a boundary Harnack inequality giving dist(x,\partial G)^{α-1} order decay for harmonic functions near the boundary. For a C^{1,β-1} open set D\subset \overline{D}\subset G, 0<α\leq (1\veeα)<β\leq 2, we prove a boundary Harnack inequality giving dist(x,\partial D)^{α/2} order decay for harmonic functions near the boundary. These inequalities are generalizations of the known results for the homogeneous case on C^{1,1} open sets. We also prove the boundary Harnack inequality for regional fractional Laplacian on Lipschitz domain.

math.PR↗
arXiv2008

Cadlag curves of SLE driven by Levy processes

Schramm Loewner Evolutions (SLE) are random increasing hulls defined through the Loewner equation driven by Brownian motion. It is known that the increasing hulls are generated by continuous curves. When the driving process is of the form \sqrtκ B+θ^{1/α}S for a Brownian motion B and a symmetric α-stable process S with κnot equal to 4 and 8, we prove that the corresponding increasing hulls are generated by Cadlag curves.

math.PR↗