We study the scrambling of quantum information in local random unitary circuits by focusing
on the tripartite information proposed by Hosur et al. We provide exact results for the …

We derive exact results for the Lindblad equation for a quantum spin chain (one-
dimensional quantum compass model) with dephasing noise. The system possesses doubly …

Let F (t, u)≡ F (u) be a formal power series in t with polynomial coefficients in u. Let F1,…, Fk
be k formal power series in t, independent of u. Assume all these series are characterized by …

Gessel walks are lattice walks in the quarter-plane $\mathbb N^ 2$ which start at the origin
$(0, 0)\in\mathbb N^ 2$ and consist only of steps chosen from the set $\{\leftarrow,\swarrow …

An m-ballot path of size n is a path on the square grid consisting of north and east steps,
starting at (0, 0), ending at (mn, n), and never going below the line {x= my}. The set of these …

We present two classes of random walks restricted to the quarter plane with non-holonomic
generating functions. The non-holonomicity is established using the iterated kernel method …

A word w= w 1⋯ wn over the set of positive integers is a Motzkin word whenever w 1= 1, 1≤
wk≤ wk− 1+ 1, and wk− 1≠ wk for k= 2,…, n. It can be associated to a n-column Motzkin …

We address the enumeration of properly q-colored planar maps, or more precisely, the
enumeration of rooted planar maps M weighted by their chromatic polynomial χM (q) and …

This work considers the nature of generating functions of random lattice walks restricted to
the first quadrant. In particular, we find combinatorial criteria to decide if related series are …

Based on the kernel method, we present systematic methods to solve equation systems on
generating functions of two variables. Using these methods, we get the generating functions …