News!

I will be joining the combinatorics group at The Mathematics Institute at Reykjavik University on Iceland in early August 2008.

History

Born in Haparanda, Sweden.
Undergraduate studies in Luleå (one year) and Uppsala, Sweden.
Master of Science in Mathematics 1999.
PhD-Student in Uppsala. Advisor Sven Erick Alm.
PhD in Mathematical Statistics 2004.
MASCOS research fellow, Melbourne, Australia 2004-2008.

Research interests

The keywords from my thesis were:

• Percolation,
• Self-avoiding walks, and
• Archimedean and Laves Lattices

Latetly I have been working on:

• Lattice paths (Dyck, Motzkin)
• Patterns in permutations
• Asymmetric Exclusion Processes
• The ECO method

Talks

Some recent talks:

• Exclusion Processes. Lattice Paths. Permutations. MASCOS research workshop.
• Cycles and patterns in permutations, lattice paths, and exclusion processes. Complex Systems seminar, The University of Melbourne.
• The (extended) ECO method. StatMech/Combinatorics seminar, UoM.
• Combinatorial enumeration with the ECO method. Talk at the Australian Mathematical Society meeting 2007.
• Constant term methods for lattice paths and their applications to Asymmetric Exclusion processes. Combinatorics seminar, Royal Technical University, Stockholm.
• Den asymmetriska exklusionsprocessen. Mathematical statistics seminar, Uppsala Univeristy, Uppsala.

Publications

Theses

Master: Lower and Upper Bounds for the Time-Constant of First-Passage Percolation

Licenciate: Probability on Graphs

Doctorate: Connectivity Properties of Archimedean and Laves Lattices.

Journal papers

[1] Lower and Upper Bounds for the Time-Constant of First-Passage Percolation. Sven Eick Alm and Robert Parviainen. Comb. Prob. Comp. 11, 433-445, 2002.

[2] Random Assignment with Integer Costs. Robert Parviainen. Comb. Prob. Comp. 13, 103-113, 2004.

[3] Bounds for the Connective Constant of the Hexagonal Lattice. Sven Erick Alm and Robert Parviainen. J. Phys. A. 37(3), 549-560, 2004.

[4] Self-avoiding walks and trails on the 3.12.12 lattice. Anthony J. Guttmann, Robert Parviainen and Andrew Rechnizter. J. Phys. A. 38(3), 2005.

[5] Inclusions and non-inclusions among the Archimedean and Laves lattices, with applications to bond percolation thresholds. Robert Parviainen and John C, Wierman. Congr. Numer. 176, 89-128, 2005.

[6] A Combinatorial Derivation of the PASEP Stationary State. Richard Brak, Sylvie Corteel, John Essam, Robert Parviainen and Andrew Rechnitzer. Elec. J. Comb. (13) R108, 2006.

[7] Lattice Path Enumeration of Patterns with k Occurrences of the Pattern 2-13. Robert Parviainen. J. Integer Seq. Vol 9, Article 06.3.2. 2006.

[8] Permutations, Cycles, and the Pattern 2-13. Robert Parviainen. Elec. J. Comb. (13) R111, 2006.

[9] Parametric production matrices and weighted succession rules: a Dyck path example. Robert Parviainen. J. Integer S. Vol 10, Article 07.6.1. 2007.

[10] Estimation of Bond Percolation Thresholds on the Archimedean Lattices. Robert Parviainen. J. Phys. A. 40 (31), 9253-9256, 2007.

Preprints

Submitted

[*] Cycles and patterns in permutations. Robert Parviainen. arXiv:math.CO/0610616. 2006.

[*] Three bijections on set partitions. Robert Parviainen, 2007.

From my thesis

These papers were part of my PhD-thesis. Papers [A] and [B] combined is basically [5] above.

[A] Inclusions and Non-Inclusions of Archimedean and Laves Lattices. Robert Parviainen and John C. Wierman.

[B] Ordering Bond Percolation Critical Probabilities. John C. Wierman and Robert Parviainen.

[C] Pairs of Graphs with Connective Constants and Critical Probabilities in the Same Order. Robert Parviainen.

[D] Inclusions and Non-Inclusions of Matching Archimedean and Laves Lattices. Robert Parviainen.

In progress

Water Seepage in Polyurethane: a Percolation Analysis. Robert Parviainen.

Bijections by weighted generating trees. Robert Parviainen.

Banded paths with applications to ASEP. Richard Brak, John Essam, Robert Parviainen.