237 citations · 250 across the 8 of their papers we have counts for
15 papers
Towards Robust Mathematical Reasoning
Thang Luong, Dawsen Hwang, Hoang H. Nguyen +17
Finding the right north-star metrics is highly critical for advancing the mathematical reasoning capabilities of foundation models, especially given that existing evaluations are e…
The CLT in high dimensions: quantitative bounds via martingale embedding
Ronen Eldan, Dan Mikulincer, Alex Zhai
We introduce a new method for obtaining quantitative convergence rates for the central limit theorem (CLT) in a high dimensional setting. Using our method, we obtain several new bo…
Cutoff for product replacement on finite groups
Yuval Peres, Ryokichi Tanaka, Alex Zhai
We analyze a Markov chain, known as the product replacement chain, on the set of generating -tuples of a fixed finite group . We show that as , the tota…
Subpolynomial trace reconstruction for random strings and arbitrary deletion probability
Nina Holden, Robin Pemantle, Yuval Peres +1
The insertion-deletion channel takes as input a bit string , and outputs a string where bits have been deleted and inserted independently at random. The trac…
Average-case reconstruction for the deletion channel: subpolynomially many traces suffice
Yuval Peres, Alex Zhai
The deletion channel takes as input a bit string , and deletes each bit independently with probability , yielding a shorter string. The trace reconstru…
Zero Sets for Spaces of Analytic Functions
Russell Lyons, Alex Zhai
We show that under mild conditions, a Gaussian analytic function that a.s. does not belong to a given weighted Bergman space or Bargmann-Fock space has the property…
Gravitational allocation for uniform points on the sphere
Nina Holden, Yuval Peres, Alex Zhai
Given a collection of points on a sphere of surface area , a fair allocation is a partition of the sphere into parts each of area , and…
When multiplicative noise stymies control
Jian Ding, Yuval Peres, Gireeja Ranade +1
We consider the stabilization of an unstable discrete-time linear system that is observed over a channel corrupted by continuous multiplicative noise. Our main result shows that if…
A high-dimensional CLT in distance with near optimal convergence rate
Alex Zhai
Let be i.i.d. random vectors in with . Then, we show that converges to a Gaussian in quad…
Surprise probabilities in Markov chains
James Norris, Yuval Peres, Alex Zhai
In a Markov chain started at a state , the hitting time is the first time that the chain reaches another state . We study the probability that…
Exponential concentration of cover times
Alex Zhai
We prove an exponential concentration bound for cover times of general graphs in terms of the Gaussian free field, extending the work of Ding-Lee-Peres and Ding. The estimate is as…
On multiple peaks and moderate deviations for supremum of Gaussian field
Jian Ding, Ronen Eldan, Alex Zhai
We prove two theorems concerning extreme values of general Gaussian fields. Our first theorem concerns with the concept of multiple peaks. A theorem of Chatterjee states that when…
Fibonacci-like growth of numerical semigroups of a given genus
Alex Zhai
We give an asymptotic estimate of the number of numerical semigroups of a given genus. In particular, if is the number of numerical semigroups of genus , we prove that $n_…
An asymptotic result concerning a question of Wilf
Alex Zhai
Let be a numerical semigroup with embedding dimension . Define to be one plus the largest integer not in , and define to be the number of elements in $Λ…
Robust Quantum State Transfer in Random Unpolarized Spin Chains
Norman Y. Yao, Liang Jiang, Alexey V. Gorshkov +4
We propose and analyze a new approach for quantum state transfer between remote spin qubits. Specifically, we demonstrate that coherent quantum coupling between remote qubits can b…