Marcus Michelen

collaborators

11 papers

quant-ph2026

Entangled states are typically incomparable

Vishesh Jain, Matthew Kwan, Marcus Michelen

Consider a bipartite quantum system, where Alice and Bob jointly possess a pure state $∣ I ¨ ⟩$ . Using local quantum operations on their respective subsystems, and unlimited cla…

math.CO2026

A polynomial improvement for the odd cycle-complete Ramsey numbers

Marcelo Campos, Matthew Jenssen, Marcus Michelen +2

We give a polynomial improvement to the cycle-complete Ramsey numbers \[ r(C_{\ell},K_k) \geq k^{1+1/(\ell- 2) + \varepsilon_{\ell} + o(1)}, \] for all fixed odd $ℓ > 7$ with $k…

math.PR2026

A simple proof of local universality for roots of Kac polynomials

Marcus Michelen, Oren Yakir

Let $f_{n}$ be a random polynomial of degree $n$ with i.i.d. mean-zero and finite variance random coefficients. It is well known that the roots of $f_{n}$ cluster uniformly around the…

math.CO2026

The largest $K_{r}$ -free set of vertices in a random graph

Tom Bohman, Marcus Michelen, Dhruv Mubayi

For $r \geq 2$ and a graph $G$ , let $I^\pm_{r} (G)$ be the maximum number of vertices in a $K_{r}$ -free subgraph of $G$ . We investigate the value $I^\pm_{r} (G)$ when $G$ is the random graph…

math.CO2026

Comparability of random permutations in the strong Bruhat order

Nicholas Christo, Marcus Michelen

The (strong) Bruhat order for permutations provides a partial ordering defined as follows: two permutations are comparable if one can be obtained from the other by a sequence of ad…

math.CO2026

The random stable roommates problem typically has no solution

Byron Chin, Marcus Michelen

Assume that $n = 2 k$ potential roommates each have an ordered preference of the $n - 1$ others. A stable matching is a perfect matching of the $n$ roommates in which no two unmatched…

Entangled states are typically incomparable

A polynomial improvement for the odd cycle-complete Ramsey numbers

A simple proof of local universality for roots of Kac polynomials

The largest Kr​-free set of vertices in a random graph

Comparability of random permutations in the strong Bruhat order

The random stable roommates problem typically has no solution

The largest $K_{r}$ -free set of vertices in a random graph