Research
Research
Research
Research
39,113+ open-access research outputs.
We study the melting of a domain wall in the quantum simple exclusion process with all-to-all hoppings (a.k.a. the charged SYK$_2$ model). We show that the real-time dynamics of physical quantities of…
We study how long the SIRS process persists or how quickly it reaches extinction across various network topologies. Our results provide a three-part characterization of this process: In finite sparse …
Responsible AI research typically focuses on examining the use and impacts of deployed AI systems. Yet, there is currently limited visibility into the pre-deployment decisions to pursue building such …
Linear mixed models are widely used to analyze non-independent data, but inference for fixed effects can be unreliable under misspecification of the random-effects distribution, inaccurate Fisher info…
Let $X_1,\ldots,X_n$ be independent random points in the closed unit ball of $\mathbb{R}^d$. Assume that each $X_i$ has a beta distribution with parameter $\beta_i \ge -1$: if $\beta_i>-1$, then $X_i$…
Generative AI is being increasingly integrated into web search for the convenience it provides users. In this work, we aim to understand how generative AI disrupts web search by retrieving and present…
The fractional stable motion is a prototypical stochastic process exhibiting both heavy tails and long-range dependence, parameterized via a stability index $\alpha$ and a Hurst exponent $H$. We consi…
We present two complementary proofs that, if the lengths of $n$ sticks are sampled at random, then the probability that no $p+1$ sticks can form a $(p+1)$-sided polygon can be expressed as the product…
Let $Z=\{Z(t): t\in \mathbb R\}$ be a stochastic process with trajectories in space $\mathbb D (\mathbb R)$. It is assumed that there exists an essentially smooth function $A:\mathbb R\to (-\infty, \i…
Under what condition is a random constraint satisfaction problem hard to refute by the sum-of-squares (SoS) algorithm? A sufficient condition is t-wise uniformity, that is, each constraint has a t-wis…
We introduce root-to-leaf path random walks on double covers of graded signed graphs and analyze their behavior in a general setting. Viewing simplicial complexes within this framework, we show that t…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 …
Euclidean random matrices arise in a wide range of physical systems where interactions are determined by spatial configurations, including disordered media and cooperative phenomena in atomic ensemble…
I propose the \emph{Random Cloud} method, a training-free approach to neural architecture search that discovers minimal feedforward network topologies through stochastic exploration and progressive st…
Self-propelled particles serve as minimal models for emulating the dynamic self-organization of microorganisms, yet most synthetic systems remain limited to a single mode of motion, namely active Brow…
Random numbers sequences (RNSs) play a vital role in various scientific and engineering applications. They are critical to the integrity of classical and quantum cryptography, the accuracy of mathemat…
We study the central limit theorem (CLT) for linear eigenvalue statistics of several types of matrix models, whose entries are having exploding moments, i.e., moments of the entries are increasing wit…
We consider the symmetric Markov random flight $\bold X(t), \; t>0,$ in the Euclidean space $\Bbb R^m, \; m\ge 3$, performed by a particle that moves in $\Bbb R^m$ with constant finite speed and chang…
Random lasing exploits multiple scattering to provide optical feedback without conventional resonant cavities, enabling simplified architectures that are readily integrated into compact photonic platf…
We study statistical properties of random numerical semigroups of a given genus. We analyze the graph of a typical numerical semigroup, understood as a function from $\mathbb{N}$ to $\mathbb{N}$. If $…
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