3 papers
math.AP2026
Novel Self-similar Finite-time Blowups with Singular Profiles of the 1D Hou-Luo Model and the 2D Boussinesq Equations: A Numerical Investigation
Bojin Chen, De Huang, Xiangyuan Li
We present novel self-similar finite-time blowup scenarios for the 1D Hou--Luo model. We numerically demonstrate that solutions that initially satisfy certain derivative degeneracy…
math.ST2025
Non-asymptotic Estimates for Markov Transition Matrices via Spectral Gap Methods
De Huang, Xiangyuan Li
We establish non-asymptotic error bounds for the classical Maximal Likelihood Estimation of the transition matrix of a given Markov chain. Meanwhile, in the reversible case, we pro…
math.PR2025
Bernstein-type Inequalities for Markov Chains and Markov Processes: A Simple and Robust Proof
De Huang, Xiangyuan Li
We establish a new Bernstein-type deviation inequality for general (non-reversible) discrete-time Markov chains via an elementary approach. More robust than existing works in the l…