A Bernoulli Gibbsian line ensemble $\mathfrak{L} = (L_1, \dots, L_N)$ is the law of trajectories $N-1$ independent random walkers $L_1, L_{N-1}$ with possibly initial and terminal locations that are conditioned to never cross each other or a given up-right path $L_N$ (i.e. $L_1 \geq \cdots L_N$). In this paper we investigate asymptotic behavior sequences ensembles $\mathfrak{L}^N (L^N_1, L^N_N)...

In this work, we evaluate quantum coherence using the $$l_{1}$$ -norm and convex-roof obtain several new results. First, provide some general triangle-like inequalities of coherence, with results better than existing ones. Second, for special three-dimensional states, a method calculating is presented. Lastly, offer distinct upper bounds in measure based on state itself.

We introduce and fully analyze a new commutation relation $\overline{K} L_1 = L_2 K$ between finite convolution integral operator $K$ differential operators $L_1$ $L_{2}$, that has implications for spectral properties of $K$. This work complements our explicit characterization commuting pairs $KL=LK$ provides an exhaustive list kernels admitting or sesquicommuting operators.

Let $p$ be an odd prime, $q=p^e$, $e \geq 1$, and $\mathbb{F} = \mathbb{F}_q$ denote the finite field of $q$ elements. $f: \mathbb{F}^2\to \mathbb{F}$ $g: \mathbb{F}^3\to functions, let $P$ $L$ two copies 3-dimensional vector space $\mathbb{F}^3$. Consider a bipartite graph $\Gamma_\mathbb{F} (f, g)$ with vertex partitions edges defined as follows: for every $(p)=(p_1,p_2,p_3)\in P$ $[l]= [l_1,...