- 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.

- (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.

- 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.

- 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.

- 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.

- 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.

- Martin Kerscher:

Morphologie großräumiger Strukturen im Universum . Dissertation an der Ludwig--Maximilians-Universität München, published by GCA-Verlag, Herdecke (1998), ISBN 3-928973-24-X, in German. - Martin Kerscher:

Simulation Mehrfachgestreuter polarisierter LIDAR Signale. Diplomarbeit and der Ludwig-Maximilians-Universität München (1994), in German.

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