13,068 research outputs found
On memory effect in modified gravity theories
In this note, we discuss the gravitational memory effect in higher derivative
and infinite derivative gravity theories and give the detailed relevant
calculations whose results were given in our recent works. We show that the
memory effect in higher derivative gravity takes the same form as in pure GR at
large distances, whereas at small distances, the results are different. We also
demonstrated that, in infinite derivative gravity, the memory is reduced via
error function as compared to Einstein's gravity. For the lower bound on the
mass scale of non-locality, the memory is essentially reproduces the usual GR
result at distances above at very small distances.Comment: 14 pages, references added, published in Turkish Journal of Physic
PP-waves as Exact Solutions to Ghost-free Infinite Derivative Gravity
We construct exact pp-wave solutions of ghost-free infinite derivative
gravity. These waves described in the Kerr-Schild form also solve the
linearized field equations of the theory. We also find an exact gravitational
shock wave with non-singular curvature invariants and with a finite limit in
the ultraviolet regime of non-locality which is in contrast to the divergent
limit in Einstein's theory.Comment: 13 pages, references added, version published in Phys. Rev.
Max-linear models on infinte graphs generated by Bernoulli bond percolation
We extend previous work of max-linear models on finite directed acyclic
graphs to infinite graphs, and investigate their relations to classical
percolation theory. We formulate results for the oriented square lattice graph
and nearest neighbor bond percolation. Focus is on the
dependence introduced by this graph into the max-linear model. As a natural
application we consider communication networks, in particular, the distribution
of extreme opinions in social networks.Comment: 18 page
The random walk on the random connection model
We study the behavior of the random walk in a continuum independent
long-range percolation model, in which two given vertices and are
connected with probability that asymptotically behaves like
with , where denotes the dimension of the underlying Euclidean
space. More precisely, focus is on the random connection model in which the
vertex set is given by the realization of a homogeneous Poisson point process.
We show that this random graph exhibits the same properties as classical
discrete long-range percolation models studied in [3] with regard to recurrence
and transience of the random walk. The recurrence results are valid for every
intensity of the Poisson point process while the transience results hold for
large enough intensity. Moreover, we address a question which is related to a
conjecture in [16] for this graph.Comment: New version of the manuscript with some extension
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