![]() ![]() In this workshop, we provide a platform where young and more senior researchers from the area of random matrices, random graphs and related topics can come together and exchange their research, find new collaborations and learn about different perspectives on the topic. A second point of focus are applications of tools stemming from random graphs theory that can be used to study the spectrum of random matrices. The recent theoretical advances in this area are remarkable and one of the key goals of the workshop is to understand the information contained in eigenvalues and eigenvectors of high-dimensional random matrices. ![]() Moreover, there has been great progess in the study of matrices which arise naturally in random graphs, like the adjacency matrix, the Laplacian matrix, or the transition matrix of the random walk on the graph. While the initial focus was on problems in statistical physics, in recent times random matrices have proven to be an important tool also in a variety of other fields like statistics, network analysis, image processing or machine learning. a piece of the graph (some of the vertices of the original graphs, and all the edges of the original graph between those vertices) that is not connected to rest of the graph, but that is itself connected.The study of matrices with random entries started in the 1950’s and has grown into an immense body of literature until today. An isolated component is a maximally connected subgraph, i.e. If a graph is not connected, it consists of several components. If a vertex doesn't have any edges it is called an isolated vertex. A simple graph doesn't need to be connected. Here is the Petersen graph, dating back to the 19th century.Ī graph is called connected if every vertex can be reached from any other vertext by traveling along edges. Here is a graph with 12 vertices and 24 edges. Simple graphs do not have edges that begin and end at the same vertex they also don't have multiple edges between any two vertices. We will study only the so-called simple graphs. Another example is given by social networks, in which we may represent people by vertices with edges linking any two friends, etc. draw an edge between them) if and only if the two teams played against each other. You can also make a graph for a sports championship, in which you use vertices to represent the teams, and you connect them (i.e. You find examples of graphs at the back of any airline in-flight magazine, in which vertices represent cities and with edges between any two cities which can be reached from each other by a non-stop flight. To distinguish them from just random edge crossings. Generally, the edges are allowed toĬross in a drawing (because it may be impossible to draw lines for all the relationships without ever crossing) the vertices are shown as fairly fat dots Line (or curve) connects any two vertices representing objects that are related or adjacent such a line is called an edge. To each other in some way, and of these relationships. A graph is a slightlyĪbstract represention of some objects that are related The basic objects in graph theory are graphs. ![]()
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