### Department of Mathematics and Systems Analysis

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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.

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**19.12. 16:15 Christian Webb (Aalto University): When is a random variable close to being normally distributed? (further info) – U3****19.12. 15:15 Alexandre Proutiere (KTH, Stockholm): Clustering in Block Markov Chains (further info) – U3****19.12. 14:00 Stefan Geiss (University of Jyväskylä): Approximation of stochastic integrals, Riemann-Liouville operators, and bounded mean oscillation (further info) – U3****19.12. 13:00 Mari Myllymäki (Natural Resources Institute Finland (Luke)): Global envelopes for testing with functional test statistics and functional data analysis (further info) – U3****19.12. 11:00 Ioan Manolescu (Université de Fribourg): Uniform Lipschitz functions on the triangular lattice have logarithmic variations (further info) – U3****19.12. 10:00 Luis Alvarez Esteban (University of Turku): A Class of Solvable Stationary Singular Stochastic Control Problems of Linear Diffusions (further info) – U3**- 18.12. 15:15 Joonas Laihanen: A distribution-based subpopulation framework for statistic estimation – M2 (M233)
- 17.12. 15:00 Istvan Prause: Arctic curves beyond the arctic circle – M3 (M234)
The dimer model studies random configurations of perfect matchings (dimer covers) of bipartite planar graphs. Through an associated height function such a configuration is encoded in a random surface. These random surfaces (with a fixed boundary) exhibit limit shape formation: a deterministic limit surface emerges in the macroscopic limit. The imposed boundary condition can have dramatic effect: in certain regions the dimers line up in an ordered fashion (form a frozen facet) and do not look random at all. A prime example of this phenomenon is the arctic circle of domino tilings of the Aztec diamond from 1995. We now have, mostly due to Kenyon et al., a general theory which describes these phenomena in unprecedented detail. The limit shape is described by a convex but singular and degenerate variational problem with a gradient constraint. These features are responsible for facet formation and the appearance of arctic curves. In the talk, I will use the lozenge tiling model (dimer model on the hexagonal lattice) to showcase these issues and address how one can analyse the variational problem.

- 14.12. 11:15 Johan Salmelin (Aalto): Energy disaggregation of electric heating appliances (MSc thesis talk) – M3 (M234)
- 10.12. 15:15 Antti Pöllänen (Aalto): Optimization of dense Wi-Fi networks via Markov chain models – M3 (M234)
MSc thesis presentation.

- 3.12. 15:15 Eveliina Peltola (University of Geneva): Crossing Probabilities of Multiple Ising Interfaces – M3 (M234)
Crossing Probabilities of Multiple Ising Interfaces The planar Ising model is one of the most studied lattice models in statistical physics. Exhibiting a continuous phase transition, it enjoys conformal invariance in the scaling limit, as has been verified recently in celebrated works initiated by S. Smirnov. In this talk, I discuss crossing probabilities of multiple interfaces in the critical Ising model with alternating boundary conditions. In the scaling limit, they are conformally invariant expressions given by so-called pure partition functions of multiple SLE(kappa) with kappa=3. I also describe analogous results for critical percolation and the Gaussian free field. Joint work with Hao Wu (Yau Mathematical Sciences Center, Tsinghua University)

- 30.8. 11:15 Marco Fiorucci (Ca' Foscari U, Venice): Graph Summarization Using Regular Partitions – M3 (M234)
The world we live in is becoming more and more interconnected and huge amounts of data are produced and stored every day by different interrelated entities. This high-throughput generation calls for the development of efficient algorithms to understand and process large and noisy network data. To address this challenging task, we develop a principled approach to summarize (compress) large graphs based on regular partitions, the existence of which was first established in a celebrated result proved by Endre Szemerédi in the mid-1970. A regular partition is defined as a partition of the vertex set into a bounded number of random-like bipartite graphs, called regular pairs. In particular, a regular pair is a highly uniform bipartite graph in which the density of any reasonably sized subgraphs is about the same as the overall density of the bipartite graph. In this talk, I will provide an overview of the regularity lemma and will discuss its potential usefulness in real-world applications.

- 22.8. 15:15 Katri Ailus: On modeling train energy consumption (Master's thesis presentation) – M3 (M234)
- 15.8. 14:15 Sung Chul Park (EPFL): Local correlations in the critical and near-critical planar Ising model – M3 (M234)
The scaling limit of the 2D critical Ising model is expected to exhibit conformal invariance, which has been proved in the case of spin (Chelkak, Hongler and Izyurov 2015) and energy (local 2-point) correlations (Hongler and Smirnov 2013). We extend these results by giving a conformally covariant description for the local n-point correlations in the scaling limit. Then we will go on to discuss preliminary results and ongoing work in the near-critical (scaling towards criticality) setting and their significance from the viewpoint of Conformal Field Theory. Based on joint work with R. Gheissari (first part) and C. Hongler.

- 8.8. 16:30 Kalle Kytölä [Math physics afternoon]: Probabilistic lattice models and conformal field theory – M3 (M234)
A major conjecture in two-dimensional statistical mechanics is that scaling limits of lattice models are described by conformally invariant quantum field theories. The main ingredient of conformal field theories is a Virasoro algebra representation on local fields. In two lattice models, the critical Ising model and the discrete Gaussian free field, we find this exact structure even before passing to the scaling limit. The result is joint work with Clément Hongler (EPFL) and Fredrik Viklund (KTH).

- 8.8. 16:00 Christian Webb [Math physics afternoon]: On the eigenvalues of a random Hermitian matrix – M3 (M234)
I will discuss some recent work concerning rigidity of eigenvalues of a random Hermitian matrix: that is, how much can the eigenvalues of a large random Hermitian matrix fluctuate around certain deterministic quantities.

- 8.8. 15:30 David Radnell [Math physics afternoon]: Moduli spaces in conformal field theory – M3 (M234)
One of the standard axiomatic approaches to conformal field theory involves infinite-dimensional moduli spaces of Riemann surfaces. The rigorous definition and study of these moduli spaces requires complex analysis and geometry, quasiconformal Teichmueller theory, functional analysis etc. I will outline the connection between these topics and state some recent results.

- 8.8. 14:30 Alex Karrila [Math physics afternoon]: On the weak convergence of multiple plane curves – M3 (M234)
In statistical mechanics, one often studies a random model on a fine-mesh lattice approximating a continuum domain. One descriptive feature of such models are interface curves, such as boundaries of magnetization clusters in a ferromagnetism model. Consider a situation where boundary conditions, for instance alternating +/- magnetizations on the boundary of the ferromagnet, force the existence of multiple macroscopic chordal interfaces. We derive criteria, valid for various random models, that guarantee the existence of a weak limit of such chordal interfaces as the lattice mesh turns finer.

- 8.8. 14:00 Armando Gutierrez [Math physics afternoon]: On the metric compactification of Banach spaces – M3 (M234)
I will explain a method that has recently appeared in metric geometry and has shown to be an effective technique to compactify metric spaces. Afterwards, I will present a complete description of the metric compactification of the classical Banach spaces Lp in finite and infinite dimensions.

- 8.8. 13:15 Antti Suominen [Math physics afternoon]: Spin correlation functions of the 2D Ising model [MSc talk] – M3 (M234)
I will discuss how discrete complex analysis and orthogonal polynomials can be used to study the spin correlation functions of the two dimensional Ising model.

- 8.8. 12:30 Osama Abuzaid [Math physics afternoon]: Infinite self avoiding half space random walks [MSc talk] – M3 (M234)
A self avoiding walk (SAW) is an injective walk in a lattice embedded in an Euclidean space. A random SAW of length n is a uniformly distributed random variable on all self avoiding walks of length n starting from origin. In this talk, we are mainly interested in random SAWs in a d-dimensional qubic lattice which are restricted to the upper half plane. These are called self avoiding half space random walks (SAHSW). I will present necessary tools to show the existence of an infinite random SAHSW which is defined as the limit of random SAHSWs of length n, as n tends to infinity.

- 19.3. 15:15 Ari-Pekka Perkkiö (LMU Munich): Optional projection in duality – M203
In this talks we characterize topological duals of Frechet spaces of stochastic processes. This is done by analyzing the optional projection on spaces of cadlag processes whose pathwise supremum norm belongs to a given Frechet space of random variables. We employ functional analytic arguments that unify various results in the duality theory of stochastic processes and also yields new ones of both practical and theoretical interest. In particular, we find an explicit characterization of dual of the Banach space of adapted cadlag processes of class (D). When specialized to regular processes, we obtain a simple proof of a result of Bismut on projections of continuous processes.

- 7.2. 17:00 Stanislav Nagy (Charles University): Unified approach to the theory of functional data depth – M3 (M234)
Depth has become a quite popular concept in functional data analysis. In the talk we discuss its general framework. We show that most known functional depths can be classified into few groups, within which they share similar theoretical properties. We focus on uniform consistency results for the sample versions of these functionals, and demonstrate that some well-known approaches to depth assessment are hardly theoretically adequate.

- 7.2. 16:15 Joni Virta (Aalto SCI): Independent component analysis of multivariate functional data – M3 (M234)
We extend a classic method of independent component analysis, the fourth order blind identification (FOBI), to vector-valued functional data. The use of multivariate instead of univariate functions allows for natural definitions for both the marginals of a random function and their mutual independence. Our model assumes that the observed functions are mixtures of latent independent functions residing in suitable Hilbert spaces, mixed with a bounded linear operator from the product space to itself. To enable the inversion of the covariance operator we make the assumption that the dependency between the mixed component functions lies in a finite-dimensional subspace. In this subspace we define fourth cross-cumulant operators and use them to construct a novel Fisher consistent method for solving the independent component problem for vector-valued functions. Finally, both simulations and an application to hand gesture data set are used to demonstrate the advantages of the proposed method over its closest competitors.

- 7.2. 15:00 Sami Helander (Aalto SCI): On typicality of functional observations – M3 (M234)
Most of the functional depth approaches presented in the literature are solely interested in the -pointwise- centrality of the observations as a measure of (global) centrality. As a result, they are missing some important features inherent to functional data such as variation in shape, roughness or range. Thus, due to the richness of functional data, we opt to talk about typicality rather than centrality of an observation. We discuss assessing typicality of functional observations. Moreover, we provide a new concept of depth for functional data. It is based on a new multivariate Pareto depth applied after mapping the functional observations to a vector of statistics of interest. These quantities allow incorporating the inherent features of the distribution, such as shape or roughness. In particular, in contrast to most existing functional depths, the method is not limited to centrality only. Properties of the new depth are explored and the benefits of a flexible choice of features are illustrated.

- 7.2. 14:15 Germain Van Bever (Université libre de Bruxelles): Halfspace depths for scatter, concentration and shape matrices – M3 (M234)
We propose halfspace depth concepts for scatter, concentration and shape matrices. For scatter matrices, our concept extends the one from Chen, Gao and Ren (2015) to the non-centered case, and is in the same spirit as the one in Zhang (2002). Rather than focusing, as in these earlier works, on deepest scatter matrices, we thoroughly investigate the properties of the proposed depth and of the corresponding depth regions. We do so under minimal assumptions and, in particular, we do not restrict to elliptical distributions nor to absolutely continuous distributions. Interestingly, fully understanding scatter halfspace depth requires considering different geometries/topologies on the space of scatter matrices. We also discuss, in the spirit of Zuo and Serfling (2000), the structural properties a scatter depth should satisfy, and investigate whether or not these are met by the proposed depth. As mentioned above, companion concepts of depth for concentration matrices and shape matrices are also proposed and studied.

- 30.1. 10:00 Teemu Murtola (University of Tampere, Faculty of Medicine and Life Sciences): Benefits of cholesterol-lowering statins in prostate cancer – M3 (M234)
Many commonly used drugs target intracellular signaling pathways that have importance in carcinogenesis and progression of cancer. One example is the mevalonate pathway which is targeted by cholesterol-lowering statin drugs. Examining possible anticancer effects of drug groups established for other indications requires comprehensive multidisciplinary approach including epidemiological studies to explore associations with cancer risk and prognosis, experimental laboratory studies to elucidate possible anticancer mechanisms and ultimately clinical trials to test for clinical benefit. This lecture describes such project testing statins' effects against prostate cancer.

- 29.1. 15:15 Jari Miettinen (Aalto ELEC): Independent component analysis for graph data using graph-autocorrelation matrices – M3 (M234)
The first independent component analysis estimators were designed for i.i.d. data, and they assume that at most one of the independent components has Gaussian density. Afterwards, methods have been developed for data with dependencies between the observations, including for example time series and spatial data. Those methods utilize solely or partially the structure of the data. For the most general case, graph data, Blochl et al. introduced an ICA estimator called GraDe (graph decorrelation) which uses approximate joint diagonalization of graph-autocorrelation matrices. GraDe contains the best-known time series and spatial methods as special cases. The structure of the graph is given in an adjacency matrix which is to be known or estimated prior to performing the ICA task. As one example in our paper on the effects of adjacency matrix estimation errors in graph signal processing, we study how the GraDe method is affected by misspecification of the adjacency matrix, using both theoretical and simulation results.

- 22.1. 15:15 Mindaugas Bloznelis (U Vilnius): Local probabilities of randomly stopped sums of power law lattice random variables and clustering patterns in complex networks – M3 (M234)
Let $X_1$ and $N$ be non-negative integer valued power law random variables. For a randomly stopped sum $S_N=X_1+\cdots+X_N$ of independent and identically distributed copies of $X_1$ we establish a first order asymptotics of the local probabilities $P(S_N=t)$ as $t\to+\infty$. Using this result we show the $k^{-\delta}$, $0\le \delta\le 1$ scaling of the local clustering coefficient (of a randomly selected vertex of degree $k$) in a power law affiliation network. http://arxiv.org/abs/1801.01035

- 19.12.2017 15:45 Eveliina Peltola (University of Geneva): Multiple SLEs for \kappa \leq 4 (further info) – U3
- 19.12.2017 14:30 Mikko Pakkanen (Imperial College London): Rough volatility: towards efficient Monte Carlo pricing and calibration (further info) – U3
- 19.12.2017 13:30 Roland Bauerschmidt (University of Cambridge): Eigenvectors and spectral measure of random regular graphs of fixed degree (further info) – U3
- 19.12.2017 11:15 Lauri Viitasaari (University of Helsinki): On model fitting and estimation of stationary processes (further info) – U3
- 19.12.2017 10:15 Aristides Gionis (Aalto University): Mining temporal networks (further info) – U3

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