Aalto Stochastics and Statistics Seminar is organized by Pauliina Ilmonen, Kalle Kytölä, and Lasse Leskelä. Feel free to contact one of us if you are interested in giving a talk.
A simple mathematical model for information spreading is a complete graph where everyone knows everyone and everyone relays messages at random time instants to randomly chosen neighbours independently of each other. In this talk we will consider information spreading in the large configuration model, which is a more advanced model. One of the key quantity analysing the rumour spreading speed is the broadcast time, the time when the rumour has reached the entire population. We will also discuss the broadcast time taking into account the passive and active users.
A physics principle asserts that the scaling limit of a critical lattice model, as increasingly dense lattices approximate a continuum domain, is described by a conformal field theory (CFT). The aim of this talk is to prove rigorously conformal invariance properties in the scaling limit of the uniform spanning tree (UST) of a planar graph, i.e., a tree subgraph that covers all the vertices of the original graph, chosen uniformly at random. In a spanning tree, any two vertices are connected by a unique path, called a branch. We study multiple simultaneous UST boundary-to-boundary branches between given boundary vertices, as well as the boundary visits of a single such branch. The related probabilities have conformally invariant scaling limits, and solve partial differential equations as predicted by CFT. As a collection of curves, such multiple simultaneous branches converge weakly to a conformally invariant law, called the local multiple SLE(2). These are among the first verifications of third-order PDEs of CFT, as well as convergence results to multiple SLE.
The horofunction compactification is the result of making any metric space into a compact topological space by only using the metric. The elements of this compactification have been recently shown to be very useful in the study of limit theorems for deterministic and random dynamical systems. In this talk I will give a complete description of the horofunction compactification of the classical lp spaces. I will also consider Hilbert's projective metric on the standard cone of positive real vectors, and describe its horofunction compactification. The latter will be used to give a new proof of the well-known Perron theorem.
For a long time network science concentrated on static graphs as representations of networked systems. This abstraction was used to analyse shortest path lengths, spreading of disease or information in networks, and many other things. Often the underlying assumption behind such analysis was that the activation of nodes and links is controlled by homogeneous Poisson processes. More recently there has been growing interest in analysing 'temporal networks' where the link activation times are determined directly from data. In this talk I will illustrate how this approach can be used to analyse a large communication network with hundreds of millions of link activation events. I will focus on how 'reference models', in which the data is shuffled in various ways, can be used for this data and how they are used in the literature on temporal networks in general. I will also discuss the challenges in the literature that are caused by the sudden increase in use of such shuffling methods of temporal network.
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