Related papers: The interchange process with reversals on the comp…
This paper concerns the long term behaviour of a growth model describing a random sequential allocation of particles on a finite cycle graph. The model can be regarded as a reinforced urn model with graph-based interactions. It is motivated…
It is widely believed that certain simple modifications of the random graph process lead to discontinuous phase transitions. In particular, starting with the empty graph on $n$ vertices, suppose that at each step two pairs of vertices are…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
We consider an inverse problem for Schr\"odinger operators on a connected equilateral graph $G$ with standard matching conditions. The graph $G$ consists of at least two odd cycles glued together at a common vertex. We prove an Ambarzumian…
We study synchronization of random one-dimensional linear maps for which the Lyapunov exponent can be calculated exactly. Certain aspects of the dynamics of these maps are explained using their relation with a random walk. We confirm that…
Weighted reciprocity between two agents can be defined as the minimum of sending and receiving value in their bilateral relationship. In financial networks, such reciprocity characterizes the importance of individual banks as both liquidity…
We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative…
We consider random permutations on $\Sn$ with logarithmic growing cycles weights and study asymptotic behavior as the length $n$ tends to infinity. We show that the cycle count process converges to a vector of independent Poisson variables…
The study of sorting permutations by block interchanges has recently been stimulated by a phenomenon observed in the genome maintenance of certain ciliate species. The result was the identification of a block interchange operation that…
We investigate a simple model corresponding to particles driven in opposite directions and interacting via a repulsive potential. The particles move off-lattice on a periodic strip and are subject to random forces as well. We show that this…
We present exact solutions for the size of the giant connected component (GCC) of graphs composed of higher-order homogeneous cycles, including weak cycles and cliques, following bond percolation. We use our theoretical result to find the…
In this paper we are concerned with the contact process with random recovery rates and edge weights on complete graph with $n$ vertices. We show that the model has a critical value which is inversely proportional to the product of the mean…
The reconfiguration problem for homomorphisms of digraphs to a reflexive digraph cycle, which amounts to deciding if a `reconfiguration graph' is connected, is known to by polynomially time solvable via a greedy algorithm based on certain…
The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system.…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
We analyze the role of the interplay between on-site interaction and inhomogeneous diffusion on the phenomenon of condensation in the zero-range process. We predict a universal phase diagram in the plane of two exponents, respectively…
We find the Ramsey number of a cycle vs. a complete graph when the order of the cycle is at least 4 times as large as the order of the complete graph. This partially confirms a conjecture of Erd\H{o}s, Faudree, Rousseau, and Schelp made in…
We consider homological edge percolation on a sequence $(\mathcal{G}_t)_t$ of finite graphs covered by an infinite (quasi)transitive graph $\mathcal{H}$, and weakly convergent to $\mathcal{H}$. Namely, we use the covering maps to classify…
We introduce a simple zero-range process with constant rates and one fast rate for a particular occupation number, which diverges with the system size. Surprisingly, this minor modification induces a condensation transition in the…
Periodic reversals of the direction of motion in systems of self-propelled rod shaped bacteria enable them to effectively resolve traffic jams formed during swarming and maximize their swarming rate. In this paper, a connection is found…