Throughout this post $\mathbb{K}$ will stand for either $\mathbb{R}$ or $\mathbb{C}$. Given $A\in\mathbb{K}^{N\times M}$, the Phase Retrieval Problem aims to recover a vector $x\in\mathbb{K}^M$ fr...

For a graph $G = (V, E)$, the clique number $\omega(G)$ and the chromatic number $\chi(G)$ are fundamental properties studied in combinatorics and graph theory. It is known that computing these qua...

Consider symmetric deterministic tensors $T_1, \ldots, T_n \in (\mathbb{R}^d)^{\otimes r}$ and let $g_1, \ldots, g_n$ be i.i.d. standard gaussian random variables. We are interested in determining ...

In recent years, significant progress has been made in understanding the mixing behavior of Glauber dynamics for Ising models, particularly in the Sherrington-Kirkpatrick (SK) model. Despite the cl...

In September 2024, at a conference on Mathematical Aspects of Learning Theory in Barcelona, Dan Spielman gave a beautiful talk on discrepancy theory and some of its applications in clinical trials....

In 2014, Andrea Montanari and Emile Richard (Montanari & Richard, 2014) proposed a statistical model for understanding a variant of Principal Component Analysis in Tensor data. This is currentl...

In the study of average-case complexity, one is often interested in the critical threshold of the signal-to-noise ratio at which a problem becomes tractable. In this post, we will consider a multi...

In this post I will discuss a seemingly simple question of high-dimensional stochastic geometry, which originated (as far as I know) in the series of works (Saunderson, 2011), (Saunderson et al., ...

In the 17th century, Christiaan Huygens (inventor of the pendulum clock) observed that pendulum clocks have a tendency to spontaneously synchronize when hung on the same board. This phenomenon of s...

Welcome to Randomstrasse101, a math blog based out of a nearly homonymous address (see more at the About). As there will be a special emphasis on open problems, I chose to start with one of my fav...