Sam Vaseghi

A commutator estimate for the Golden–Thompson gap in qubit chains

For a finite qubit chain with bounded nearest-neighbor interactions, split the interaction sum into its odd and even bond layers $A$ and $B$. We compare the logarithmic trace gap $F(\beta)=\log\{\tau(e^{\beta A}e^{\beta B})/\tau(e^{\beta(A+B)})\}$ with $\mathcal{E}=\tau([A,B]^*[A...

A dimension-independent box bound from dual total correlation

Let $S$ be a finite nonempty set in a product of $d$ coordinate spaces, and let $\mathrm{U}_S$ be its uniform law. We prove that some nonempty Cartesian box $B$ satisfies $ |S\triangle B|\leq 10\mathrm{DTC}(\mathrm{U}_S)|S|, $ where dual total correlation is computed using natura...

A local-degree entropy bound for systematic Gibbs scans

Let \(P_1,\ldots,P_n\) be the single-site heat-bath operators of a finite probability law. Suppose that \(\operatorname{Ent}_{\mu}(g^2)\leq L\sum_{i=1}^{n}\lVert(I-P_i)g\rVert_2^2\) and that each update fails to commute with at most \(\Delta\) others. We prove that every ordered...

A uniform logarithmic lower bound for cyclovariety Mahler measures

Let \(C_k\) be the cyclovariety associated with all \(k\)-th roots of unity in the construction of Cornelissen, Hokken and Ringeling. We prove, for every integer \(k\ge 2\),\[\mathrm{m}(C_k)\ge\frac16\log k-\frac14+\frac1{3k}-\frac1{12k^2}.\]Together with the known upper bound, t...

Local return moments and certified random-solving times for Rubik's Cube

Consider the random walk on the standard $3\times3\times3$ Rubik's Cube that independently chooses one of the eighteen face turns with equal probability. Let $N$ denote the number of legal configurations and let $T_e$ be the first hitting time of the solved configuration, includi...

Local return moments and certified random-solving times for Rubik's Cube

Consider the random walk on the standard $3\times3\times3$ Rubik's Cube that independently chooses one of the eighteen face turns with equal probability. Let $N$ denote the number of legal configurations and let $T_e$ be the first hitting time of the solved configuration, includi...

A uniform logarithmic lower bound for cyclovariety Mahler measures

Let \(C_k\) be the cyclovariety associated with all \(k\)-th roots of unity in the construction of Cornelissen, Hokken and Ringeling. We prove, for every integer \(k\ge 2\),\[\mathrm{m}(C_k)\ge\frac16\log k-\frac14+\frac1{3k}-\frac1{12k^2}.\]Together with the known upper bound, t...