Publications of Martin Kerscher

Cosmology | Fluid Dynamics | Spatial Statistics | Meteorology

Cosmology:

• We compare marginalisation and profiling for parameter estimation and recommend marginalisation.
  Martin Kerscher and Jochen Weller.
  On marginals and profiled posteriors for cosmological parameter estimation. JCAP11(2024)035.
• Using low discrepancy sequences I show how to improve accuray and speed of estimators for the two-point correlation function.
  Martin Kerscher.
  Improving the accuracy of estimators for the two-point correlatio function. A&A 666 (2022) A181.
• We review some of the common methods for model selection.
  Martin Kerscher and Jochen Weller.
  On Model Selection in Cosmology SciPost Lecture Notes 9 (2019).
• With the scale dependent correlation coefficients the amplitude and the spatial range of conformity are determined from galaxy and halo samples.
  Martin Kerscher.
  Spatial Range of Conformity A&A 615 (2018) A109.
• A morphological analysis of the galaxy distribution nearby and a comparison with simulations.
  Martin Kerscher and Anton Tikhonov.
  Morphology of the local volume A&A 509 (2010) A57.
• I reinvestigate the SSRS2, CfA2, and the PSCz galaxy catalogues with two-point measures. The analysis of volume- and luminosity-limited subsamples shows that there is a clear signal of luminosity segregation in the optically selected catalogs, and furthermore no indication of a fractal scaling in any of these catalogs.
  Martin Kerscher:
  Luminosity segregation versus fractal scaling in the galaxy distribution, Europhys. Lett. 61 (2003), pp.856.
• In an analysis of a large N-body simulation we find strong correlations in the spin and orientation of the halos.
  Andreas Faltenbacher, Martin Kerscher, Stefan Gottlöber, and Volker Müller:
  Correlations in the orientations of galaxy clusters , A&A 395 (2002), 1-9.
• In an N-body simulations we investigate the interplay of the spatial correlations of halos with their merger histories.
  Stefan Gottloeber, Martin Kerscher, Andrey V. Kravtsov, Andreas Faltenbacher, Anatoly Klypin, Volker Mueller:
  Spatial distribution of galactic halos and their merger histories , A&A 387 (2002), 778-787.
• A review of methods, applications and models for marked point sets.
  Claus Beisbart, Martin Kerscher, and Klaus Mecke:
  Mark correlations: relating physical properties to spatial distributions, In: Morphology of Condensed Matter Physics and Geometry of Spatially Complex Systems (Eds. K. Mecke and D. Stoyan) Lecture Notes in Physics 600 (2002) p. 358-390. 
• In this paper I clarify what a Gaussian Point distribution is, and I show how to simulate it. The extension to the n-point process is given. Also an extension of the halo-model, now including halo substructure is discussed.
  Martin Kerscher,
  Constructing, characterizing, and simulating Gaussian and higher--order point distributions, PRE 64 (2001), 056109.
• Using the backreaction formalism, we show that the anisotropic collapse occurs significantly earlier compared to spherical collapse.
  Martin Kerscher, Thomas Buchert, Toshifumi Futamase:
  On the abundance of collapsed objects, ApJL 558 (2001), pp. L1.
• We quantify the Morphology of the distribution of galaxy clusters extracted from the REFLEX survey and find significant non-Gaussian features.
  M.Kerscher, K.Mecke, P.Schuecker, H. Böhringer, L.Guzzo, C.A.Collins, S.Schindler, S. De Grandi, R.Cruddace
  Non-Gaussian morphology on large scales: Minkowski functionals of the REFLEX cluster catalogue, A&A 377 (2001), pp. 1.
• Following our analysis of the 1.2Jy galaxy catalogue we find similar large morphological fluctuations in the deeper PSCz catalogue.
  Martin Kerscher, Klaus Mecke, Jens Schmalzing, Claus Beisbart, Thomas Buchert, and Herbert Wagner,
  Morphological fluctuations of large-scale structure: the PSCz survey, A&A 373 (2001), pp. 1.
• We discuss luminosity and morphological segregation using markcorrelation function.
  Claus Beisbart and Martin Kerscher:
  Luminosity- and morphology-dependent clustering of galaxies, ApJ 545 (2000), pp. 6.
• A quantitative analysis of the impact of inhomogeneities on cosmological parameters.
  Thomas Buchert, Martin Kerscher and Christian Sicka:
  Backreaction of inhomogeneities on the expansion: the evolution of cosmological parameters, PRD 62 (2000), pp. 043525.
• A review of statistical methods used in cosmology, emphasizing the importance of morphological measures.
  Martin Kerscher:
  Statistical analysis of large-scale structure in the Universe, In: Statistical Physics and Spatial Satistics: The art of analyzing and modeling spatial structures and pattern formation (Eds. K. Mecke and D. Stoyan) Lecture Notes in Physics 554 (2000) pp. 36-71.
• We compare estimators for the two-point correlation function, leading to clear recommendation: The Landy - Szalay estimator.
  Martin Kerscher, Istvan Szapudi, and Alex Szalay:
  A comparison of estimators for the two-point correlation function, ApJL, 535 (2000), pp. L13.
• Several estimators of the correlation integral and the two-point correlation function are discussed. In clarifying the geometrical nature of two-point measures, I could show how biases enter the Davis-Peebles, the Landy-Szalay and the Hamilton estimators.
  Martin Kerscher:
  The geometry of second-order statistics - biases in common estimators. A&A 343 (1999), pp. 333.
• An article about an application of the J-function to galaxy catalogues, and a comparison with a simple model of galaxy clustering. The comparison with mock-catalogues showed that a MDM model is not able to reproduce the observed clustering of galaxies.
  Martin Kerscher, Maria Jesus Pons-Borderia, Jens Schmalzing, Roberto Trasarti-Battistoni, Thomas Buchert, Vicent J. Martinez and Riccardo Valdarnini:
  A global descriptor of spatial pattern interaction in the galaxy distribution. ApJ 513 (1999), pp. 543.
• There are some indicitions for regularity on large scales, as can be seen from the distribution of superclusters.
  Martin Kerscher:
  Regularity in the distribution of superclusters? A&A 336 (1998), pp. 29-34.
• An invited talk about galaxy clustering and spatial point processes, given at the 51st meeting of the ISI (International Statistical Institute), Istanbul.
  Martin Kerscher and Vicent Martinez:
  Galaxy clustering and spatial point processes. Bull. Int. Statist. Inst. 67 no. 2 (1998), pp. 363-366.
• An analysis of the 1.2 Jy galaxy catalogue with Minkowski functionals, next neighbour distributions, and fluctuations of counts in cells, focussing on the fluctuations seen in the catalogue.
  Martin Kerscher, Jens Schmalzing, Thomas Buchert and Herbert Wagner,
  Fluctuations in the IRAS 1.2 Jy Catalogue. A&A 333 (1998), pp. 1-12.
• A profound statistical analysis of Minkowski Functionals of Abell/ACO Clusters and a comparison with several cosmological models.
  Martin Kerscher, Jens Schmalzing, Jörg Retzlaff, Stefano Borgani, Thomas Buchert, Stefan Gottlöber, Volker Müller, Manolis Plionis and Herbert Wagner:
  Minkowski functionals of Abell/ACO clusters. MNRAS 284 (1997), pp. 73-84.

Cosmology: Proceedings and other publications

• I show with an example implementation using the pair counts from corrfunc how to increase the accuray of estimators for the two-point correlation function at no extra computational cost.
  Martin Kerscher:
  Increased accuracy of the two-point correlation function at no extra cost by Martin Kerscher, (2024)
• (in German) Eine Einführung in statistischen Methoden wie sie in der Kosmologie verwendet werden.
  M. Kerscher:
  Statistische Methoden zur Beschreibung der Galaxienverteilung, Zusammenfassung des Vortrags auf der IWAA 2003.
  
• A two--page summary of our paper dealing with the non-Gaussian cluster distribution.
  M. Kerscher, K. Mecke, P. Schuecker, H. Böhringer, L. Guzzo, S. De Grandi, C. A. Collins, S. Schindler, R. Cruddace:
  Non--Gaussian morphology on large scales: Minkowski functionals of the REFLEX clusters of galaxies , poster presentation at the conference:, Tracing Cosmic Evolution With Galaxy Clusters, July 3rd-6th 2001, Sesto Pusteria, Italy
• A short introduction to Mark correlation functions.
  Martin Kerscher and Claus Beisbart:
  Mark correlations, in: Mining the Sky: Proceedings of the MPA/ESO/MPE Workshop Held at Garching, Germany, July 31 - August 4, 2000, Ed. Anthony J. Banday, Saleem Zaroubi, Matthias Bartelmann, Springer 2003
  
• A short introduction to scalar Minkowski functionals and their vector valued counterparts. The quantification of large-scale morphological fluctuations, as well as the morphological evolution of galaxy clusters illustrate their versatility.
  Claus Beisbart, Jens Schmalzing and Martin Kerscher:
  The hierarchy of Minkowski functionals for the morphometry of cosmic structure, in: Mining the Sky: Proceedings of the MPA/ESO/MPE Workshop Held at Garching, Germany, July 31 - August 4, 2000, Ed. Anthony J. Banday, Saleem Zaroubi, Matthias Bartelmann, Springer 2003
• We introduce markcorrelation function to cosmology and illustrate their behaviour in an application to the SSRS2.
  Claus Beisbart and Martin Kerscher:
  On Luminosity and Morphology segregation in the SSRS2, preprint
• We learned even more about backreaction.
  Martin Kerscher, Thomas Buchert, Christian Sicka:
  Backreaction and the evolution of cosmological parameters . Proc. of the Sixth SFB-375 Ringberg workshop, Ringberg Castle, Tegernsee, Germany, 1999.
• Following the work by Buchert and Ehlers we show that the backreaction has a significant impact on the evolution of large domains.
  Christian Sicka, Thomas Buchert and Martin Kerscher:
  Backreaction in cosmological models. Proc. of the Fifth SFB-375 Ringberg workshop, Ed. Daniel Thomas, Ringberg Castle, Tegernsee, Germany, 1999.
• This is a short review of the statistical work performed in the group B3 within the SFB-375.
  Martin Kerscher:
  Statistics of large scale structures. Proc. of the Fifth SFB-375 Ringberg workshop, Ed. Daniel Thomas, Ringberg Castle, Tegernsee, Germany, 1999.
• A proceedings article for a talk about regularity on large scales given at the 12th Potsdam Comology Workshop.
  Martin Kerscher:
  Regularity in the distribution of superclusters. Proc. Large Scale Structure: Tracks and Traces, Potsdam, Germany, Sebt. 15-19, 1997, eds. V. Müller and S. Gottlöber and J. P. Mücket and J. Wambsgans.
• Additionally to the results presented in our paper on Fluctuations in the IRAS 1.2 Jy Catalogue we discuss the error estimates and selection effects in detail and confirm the fluctuations seen in the catalogue. Furthermore we look closer at the spatial origin of the fluctuation and we compare with optically selected galaxies from the CfA1 survey.
  Martin Kerscher, Jens Schmalzing, Thomas Buchert and Herbert Wagner:
  The Significance of the Fluctuations in the IRAS 1.2 Jy Galaxy Catalogue. Proceedings of the 2nd SFB workshop on Astro-particle physics, Ringberg 1996, Report SFB375/P002, eds. R. Bender and T. Buchert and P. Schneider, pp. 83-98.
• A preliminary analysis revealing fluctuations in the IRAS 1.2Jy Catalogue.
  Martin Kerscher and Jens Schmalzing:
  Fluctuations in the IRAS 1.2Jy Catalogue. Generation of Cosmological Large Scale Sturcture (Proc. of NATO ASI, Erice, Italy, Nov. 1996), eds. Piero Galeotti and David Schramm.
  
• More on Minkowski Functionals in Cosmology.
  Jens Schmalzing and Martin Kerscher:
  Minkowski Functionals in Cosmology - A unifying approach to higher-order statistics of large-structure. Generation of Cosmological Large Scale Sturcture (Proc. of NATO ASI, Erice, Italy, Nov. 1996), eds. Piero Galeotti and David Schramm.
• A proceedings article dealing with boundary corrections for Minkowski functionals.
  Martin Kerscher, Jens Schmalzing and Thomas Buchert:
  Analyzing galaxy catalogues with Minkowski functionals. Mapping, measuring and modelling the universe, Astronomical Society of the Pacific (1996), eds. Peter Coles, Vicent Martínez and Maria Jesús Pons Borderia, pp. 247-252.
• A summer school tutorial on Minkowski functionals in Cosmology. This tutorial is a good starting point, if you are interested in Minkowski functionals.
  Jens Schmalzing, Martin Kerscher and Thomas Buchert:
  Minkowski functionals in cosmology, in: International School of Physics Enrico Fermi. Course CXXXII: Dark matter in the universe (1996), eds. Silvio Bonometto, Joel Primack and Antonello Provenzale, pp. 281-291.

Fluid Dynamics:

• We quantify the scaling of the bubble and particle clusters in a simulation of homogeneous turbulence using the Kaplan-Yorke dimenson. To sharpen our conclusions we investigate the global morphology of these clusters with Minkowski functionals.
  E. Calzavarini, M. Kerscher, D. Lohse, F. Toschi:
  Dimensionality and morphology of particle and bubble clusters in turbulent flow., JFM 607 (2008), 13-24.

Spatial Statistics:

• In this paper I clarify what a Gaussian Point distribution is, and I show how to simulate it. The extension to the n-point process is given. Also an extension of the halo-model, now including halo substructure is discussed.
  Martin Kerscher,
  Constructing, characterizing, and simulating Gaussian and higher--order point distributions, PRE 64 (2001), 056109.
• An article dealing with boundary corrections for the J-function, and why we sometimes do not need them.
  Adrian J. Baddeley, Martin Kerscher, Katja Schladitz, and Bryan T. Scott:
  Estimating the J-function without edge corrections. Statistica Neerlandica 54 (2000), pp. 1-14.

Meteorology:

• In this article we test a simplified (double scattering) approach of multiple scattering against the exact stochastic model, and derive inversion algorithms for the extinction coefficient.
  Gerhard H. Ruppersberg, Martin Kerscher, Masoud Noormohammadian, Ulrich G. Oppel, and Wolfgang Renger:
  The Influence of Multiple Scattering on Lidar Returns by Cirrus Clouds and an effective Inversion Algorithm for the Extinction Coefficient. Contributions to Atmosperic Physics 70 (1997), pp. 91-107.
• An article describing the simulation techniques for polarized LIDAR signals and a comparison with a measurement.
  Martin Kerscher, Wilhelm Krichbaumer, Masoud Noormohammadian, Ulrich G. Oppel:
  Polarized Multiply Scattered LIDAR Signals, Optical Review, 2 no.4 (1995), pp. 304-307.

Meteorology: Reports and Articles in Proceddings

• A proceedings article dealing with the simulation and inversion of space-based LIDAR signals. For the inversion we use deterministic and stochastic search procedures.
  Ulrich G. Oppel, Martin Kerscher, Heike Krasting:
  Calculation of polarized multiply scattered return signals of a space-based multichannel LIDAR and the retrieval of the extinction coefficient and the particle size distribution based on random search including a sensitivity analysis. Lidar Techniques and Remote Sensing II (1995), ed. Christian Werner, SPIE volume 2581, pp. 79-90.
• Another proceedings article dealing with the simulation and inversion of LIDAR signals.
  Martin Kerscher, Heike Krasting, Ulrich G. Oppel:
  Retrieval of environmental prarmeters from multiply scattered return signals of ground-based and airborne LIDARs. Air pollution and Visibility Measurements (LASER'95), eds. P. Fabian, V. Klein, M. Tacke, K. Weber, Ch. Werner.
• A research report to the german science foundation describing the stochastic model for multiply scatterd polarized light, the connection with transport theory and several example calculations performed with a variance reduction Monte Carlo program are discussed.
  Martin Kerscher, Masoud Noormohammadian, Ulrich G. Oppel:
  Methoden zur Bestimmung mikrophysikalischer Parameter mit einem Mehrkanal Polarisations LIDAR. Report of the Mathematical Institute of the University of Munich, (1995), in English.