11 citations · 35 across the 16 of their papers we have counts for
16 papers
-sectorial discrete Laplacians and recurrence of complex-weighted graphs
Anna Muranova
We consider complex-weighted graphs, whose edge weights belong to a sector in the complex plane. We show that the corresponding Dirichlet Laplacian is -sectorial, and, hence, ge…
Periodic discrete graphs with prescribed spectrum
Andrii Khrabustovskyi, Anna Muranova
We construct a periodic weighted graph whose discrete Laplacian has a spectrum with precisely gaps. Moreover, we show that by an appropriate choice of the weights, the endpoint…
Burnings of trees and their homologies
Yuri Muranov, Anna Muranova
The problem of graph burning was firstly introduced as a model for different processes of social and network interactions. Recently, the authors of the present paper developed meth…
On the moments of the volume for random convex chains
Anna Gusakova, Anna Muranova
Let be the triangle in the plane with vertices , and . The convex hull of points , and independent random points uniformly di…
Homology of graph burnings
Yuri Muranov, Anna Muranova
In this paper we study graph burnings using methods of algebraic topology. We prove that the time function of a burning is a graph map to a path graph. Afterwards, we define a cate…
Recurrence and transience for non-Archimedean and directed graphs
Matthias Keller, Anna Muranova
We introduce the notion of recurrence and transience for graphs over non-Archimedean ordered field. To do so we relate these graphs to random walks of directed graphs over the real…
Power iteration for matrices with power series entries
Ragon Ebker, Anna Muranova, Max Schmidt
We prove the method of power iteration for matrices with at most finite entries from the Levi-Civita field under the assumption that there exists an eigenvalue with th…
Capacity of infinite graphs over non-Archimedean ordered fields
Florian Fischer, Matthias Keller, Anna Muranova +1
In this article we study the notion of capacity of a vertex for infinite graphs over non-Archimedean fields. In contrast to graphs over the real field monotone limits do not need t…
Dual Cheeger constant for weighted graphs over ordered fields
Anna Muranova
We consider a dual Cheeger constant for finite graphs with edge weights from an arbitrary real-closed ordered field. We obtain estimates of in terms of…
Discrete Laplace and transition operators over non-Archimedean ordered fields
Anna Muranova
We investigate properties of spectrum of normalized Laplacian for finite graphs over non-Archimedean ordered fields. We prove a Cheeger's inequality for first non-zero…
Networks with complex weights: Green function and power series
Anna Muranova, Wolfgang Woess
We introduce a Green function and analogues of other related kernels for finite and infinite networks whose edge weights are complex-valued admittances with positive real part. We…
Eigenvalues of the normalized complex Laplacian on finite electrical networks
Anna Muranova, Robert Schippa
The spectrum of the normalized complex Laplacian for electrical networks is analyzed. We show that eigenvalues lie in a larger region compared to the case of the real Laplacian. We…
The effective impedances of infinite ladder networks and Dirichlet problem on graphs
Anna Muranova
We calculate effective impedances of infinite - and - ladder networks as limits of effective impedances of finite network approximations, using a new method, which involves…
On the effective impedance of finite and infinite networks
Anna Muranova
In this paper we deal with the notion of the effective impedance of AC networks consisting of resistances, coils and capacitors. Mathematically such a network is a locally finite g…
Effective Impedance over Ordered Fields
Anna Muranova
In this paper, we study properties of effective impedance of finite electrical networks and calculate the effective impedance of a finite ladder network over an ordered field. More…
On the notion of effective impedance
Anna Muranova
It is known that electrical networks with resistors are related to the Laplace operator and random walk on weighted graphs. In this paper we consider more general electrical networ…