Topics of seminar talks

Speakers and calendar of seminar talks
Last update: 07.05.2018

Dates and locations

Seminar calendar

Papers (the list may change according to the number of speakers)

Complexity levels:

Prerequisites

List of topics for the student talks

Topic 1: Continuum percolation (including signal-to-interference ratio percolation)

1.1 Signal-to-interference ratio percolation for Poisson point processes

1. + [DBT]: O. Dousse, F. Baccelli, P. Thiran. Impact of interferences on connectivity in ad-hoc networks.
   (Introduction of the SINR percolation model. Theorem 1 with proof. Phase transitions: Theorems 2 and 4 with proof sketch. Role of bounded support+boundedness of the attenuation function in these theorems. For Section IV, a short summary is enough.)
   WARNING: This paper also has a non-full version available online, in which the section "D. Asymptotic Results for Large lambda" is missing.
2. ++ (1) [DFMMT]: O. Dousse, M. Franceschetti, N. Macris, R. Meester and P. Thiran, Percolation in the signal to interference ratio graph.
   (Introducing the SINR model, conditions on the attenuation function. Percolation: Theorem 1 with sketch of proof, explaining how it improves Theorem 2 of [DBT]. How would you prove Corollary 1? Does it always hold if the attenuation function has compact support?)

1.2 Other new models of continuum percolation based on Poisson point processes

3. ++ [AT] D. Ahlberg, J. Tykesson. Gilbert's disc model with geostatistical marking.
   (Model definition. Phase transitions: Theorem 1 with sketch of proof. Overview of all results of Section 2. Free choice: proof sketch of the main result from Section 2.2, 2.3 or 2.4. Overview of Sections 3 and 5, proofs can be sketched or omitted here.)
4. +++ [DDLS] D. Coupier, D. Dereudre and S. Le Stum. Absence of percolation for Poisson outdegree-one graphs.
   (Introduction of the model, main examples. Theorem 3.1, sketch of proof from Section 4.1, and all other parts of the proof that you find important to mention, the rest can be omitted. Theorem 3.2 with main ideas of the proof.)
5. ++ [H] C. Hirsch. Bounded hop percolation.
   (Model definition. Subcritical phase: Proposition 1 + Theorem 2 with sketch of proof. Theorem 3 and its corollaries, main steps of proof. Theorem 6 with main ideas of proof, technical computations can be left out, but explain Figure 2 if it fits into time.)

1.3 Continuum percolation for non-Poissonian point processes

6. ++ [BY1] B. Błaszczyszyn, D. Yogeshwaran. Directionally Convex Ordering of Random Measures, Shot Noise Fields and Some Applications to Wireless Communications.
   (Definition of dcx ordering, Theorem 2.1 with main steps of proof. Overview of the results of Section 3. Free choice: 1--2 proofs from Section 3, 1--2 examples from Section 5 and 1--2 applications from Section 6.)
7. ++ (6) [BY2] B. Błaszczyszyn, D. Yogeshwaran. Clustering and percolation of point processes.
   (Main goals of the paper, definitions of sub-/super-Poisson processes, recalling dcx ordering from [BY1] /see 6th talk/. Theorem 1.3+results of Section 3.3 with main ideas of proof, and with the auxiliary results from Sections 2, 3.1, 3.2 if they are needed.
   Afterwards, free choice: either stating the SINR percolation results of Section 3.4 with main ideas of proof and a comparison to [DFMMT, Theorem 1], or sketching the example of Section 4 and explaining its importance.)
   For motivation why to study such SINR graphs, see also: Connectivity in sub-Poisson networks by the same authors.
8. ++ [HJC] C. Hirsch, B. Jahnel and E. Cali. Continuum percolation for Cox point processes.
   (Model definition. Phase transitions: Theorems 2.4, 2.5 with proof. Palm calculus for Cox processes. Overview of the results of Sections 2.2, the proofs of which can be sketched or completely omitted. Examples 3.1, 3.2 with the computations therein.)
9. +++ [GKP] S. Ghosh, M. Khrisnapur, Y. Peres. Continuum Percolation for Gaussian zeroes and Ginibre eigenvalues.
   PART 1 of the paper: Existence of a critical radius for the GAF process.
   (The goal of the talk is to explain and to prove the first sentence of Theorem 1.2. Definition of the GAF zero process, results of Section 3 with sketch of proof. Main steps of the proof of Theorem 1.2 [existence of a critical radius] in Section 4.1: without many technical details, but with an explanation what the Cantor set type construction is used for. The Ginibre ensemble and Section 5 about uniqueness of the infinite cluster should be left out from the talk, it is enough to read these parts. )
10. ++ [S] K. Stucki. Continuum percolation for Gibbs point processes.
    (Model definition and preliminaries from Section 2. Theorem 3.1 with Remark 3.2 and main ideas of proof, Theorem 3.3 with proof, Remark 3.4 and Example 3.5. Proposition 4.1 with proof, the discussion after the proof is not necessary.)
    This may be a useful reference: David Dereudre: Introduction to the theory of Gibbs point processes.

Topic 2: Capacity of wireless networks (follow-up works of the Gupta--Kumar paper)

11. + [GTs] M. Grossglauser, D. Tse. Mobility increases the capacity of ad-hoc networks.
    (Short overview of the results without mobility. Results of Sections III.B and III.C with proof, longer computations can be shortened. Section III.E can be omitted, and for Sections III.D, III.F and IV., a short summary is sufficient.)
12. ++ [FDTsT] M. Franceschetti, O. Dousse, D. Tse and P. Thiran. Closing the Gap in the Capacity of Wireless Networks Via Percolation Theory.
    (Main result of the paper and its relevance. Sketch of the proof, highway construction. Overview of Section VII about dense networks. Technical details can be omitted, the proof of the results in the Appendix can be left out.)

Topic 3: Time-dependence and mobility in networks (thermodynamic limit)

13. ++ [DFK] H. Döring, G. Faraud and W. König. Connection times in large ad-hoc mobile networks.
    PART 1 of the paper: Connection time of two participants in the thermodynamic limit.
    (Model definition. Theorem 1.2 with sketch of proof and interpretation (local+global constraint). Discussion of Section 1.3. Sections 1.4 and 4 should be left out from the talk, it is enough to read them.)

Requirements and auxiliary materials

Requirements for student speakers

Sample concept paper

Sample seminar report