TU Budapest -- BME

talks in Spring semester 2015 -- előadásai a 2015 tavaszi félévben

Threshold state of the abelian sandpile

Abstract

A sandpile on a graph is an integer-valued function on the vertices.
It evolves according to local moves called topplings. Some sandpiles
stabilize after a finite number of topplings, while others topple
forever. For any sandpile s_0 if we repeatedly add a grain of sand at
an independent random vertex, we eventually reach a "threshold state''
s_T that topples forever. Poghosyan, Poghosyan, Priezzhev and Ruelle
conjectured a precise value for the expected amount of sand in s_T in
the limit as s_0 tends to negative infinity. I will outline how this
conjecture was proved in
http://arxiv.org/abs/1402.3283
by means of a Markov renewal theorem. This talk will be elementary and all sandpile
terms will be defined.

2015.06.18 Thursday, 16:15

The Simple Harmonic Urn

Abstract

The simple harmonic urn is a two-colour urn model whose sample paths
approximate the phase portrait of the simple harmonic oscillator. We
start with N red balls and 0 blue balls. Each time a red ball is
picked from the urn, it is returned along with a blue ball. Each time
a blue ball is picked from the urn, it is returned and a red ball is
removed from the urn. We stop when the last red ball is removed. By
coupling the process to the renewal process with uniform inter-arrival
times, we obtain precise estimates on the mean and variance of the
number of blue balls remaining, and an exact description of its
distribution in terms of Eulerian numbers. Whenever the urn becomes
monochromatic, we can continue the process by exchanging the roles of
the two colours. Is the resulting process recurrent or transient? Come
to the talk to find out!

2015.05.07 Thursday, 16:15

Discrepancy and spectra

Abstract

I will prove relations between the k-way discrepancy md_k(C) of a
rectangular array C of nonnegative entries and its spectra. In one
direction, irrespective of the size of C, I give the following
estimate for the kth largest non-trivial singular value of the
normalized table: s_k <= 9 md_k(C) (k + 2 - 9k ln md_k(C)), provided
0 < md_k(C) < 1 and k <= rank(C). The other direction and Butler's
result for the k=1 case will also be considered. The result naturally
extends to the singular values of the normalized adjacency matrix of a
weighted undirected or directed graph.

2015.04.30 Thursday, 16:15

A dynamical approach to Pirogov-Sinai theory

Abstract

We combine the loss-network dynamics introduced in [1] with the
framework of Pirogov-Sinai theory to obtain new proofs of the
stability results given by this theory, which replace the traditional
use of cluster expansions with tools from the theory of stochastic
processes. This dynamical approach allows us to enlarge the standard
range of stability in some models while also yielding a perfect
simulation algorithm for the infinite-volume stable phases of systems
in the non-uniqueness regime.

[1] Fernández, Roberto, Ferrari, Pablo A., Garcia, Nancy L. Loss network representation of Peierls contours. Ann. Probab. 29 (2001), no. 2, 902-937.

[1] Fernández, Roberto, Ferrari, Pablo A., Garcia, Nancy L. Loss network representation of Peierls contours. Ann. Probab. 29 (2001), no. 2, 902-937.

2015.04.23 Thursday, 16:15

Non-Markovian SI spreading models on the critical Galton-Watson tree with a few extra edges (Stochastics PhD student reports)

UNUSUAL TIME / SZOKATLAN IDŐPONT

2015.04.10 Friday, 14:15

The flow of two falling balls mixes rapidly (Stochastics PhD student reports)

UNUSUAL TIME / SZOKATLAN IDŐPONT

2015.04.10 Friday, 14:40

Ergodic properties of coupled map systems (Stochastics PhD student reports)

UNUSUAL TIME / SZOKATLAN IDŐPONT

2015.04.10 Friday, 15:05

TBA (Stochastics PhD student reports)

2015.04.09 Thursday, 17:30

Error exponent for asynchronous multiple access channels (improvements since the talk of Lóránt Farkas) (Stochastics PhD student reports)

2015.04.09 Thursday, 17:05

Noise sensitivity and influential subsets for Boolean functions (Stochastics PhD student reports)

2015.04.09 Thursday, 16:40

Extending the Rash model to a multiclass parametric network model (Stochastics PhD student reports)

2015.04.02 Thursday, 16:15

Random processes with long memory -- "true" self-avoiding walk, and population generalized semi-Markov processes. PhD home defence / PhD házivédés

Abstract

We examine two different models with long memory. The true self-avoiding walk (TSAW) is a class of self-repelling random walks,
for which we prove central limit approximation using Kipnis-Varadhan technology. For a class of density-dependent population
generalized semi-Markov processes (PGSMP, a class of population models where non-Markovian transitions are also allowed),
we derive and prove the mean-field limit using probability concentration results.

2015.04.02 Thursday, 16:15

Kac-Ward matrices and the double-Ising model

Abstract

The Kac-Ward formula expresses the partition function of the Ising model on
a finite planar graph as the square root of the determinant of a certain
operator acting locally on the edges of the graph. I will first present a
new short and simple proof of this classical result. Second, I will explain
how this framework can be generalized and conveniently reinterpreted in the
context of the double-Ising model, the spin model obtained by taking the
pointwise product of +/- spins in two independent Ising models. In this model,
the interfaces separating + and - form a collection of random loops, which
have been conjectured by David Wilson to have a precise universal scaling
limit. I will present Wilson's conjecture and discuss some relevant facts in
the light of the above framework.
Joint work in progress with Dmitry Chelkak (ETH-ITS Zurich & Steklov
Institute St.Petersburg) and David Cimasoni (University of Geneva).

2015.03.05 Thursday, 16:15

Linear functional equations - Doktori védés és nyilvános vita / PhD defense and public discussion

UNUSUAL PLACE AND TIME / SZOKATLAN HELY ÉS IDŐ

2015.02.27 Friday, 14:00

Unusual place: ELTE Északi épület 7.21-es terem / ELTE North building, room 7.21.

Zero density of open paths in the Lorentz mirror model

Abstract

The Lorentz mirror model can be thought of as a percolation problem or as a
deterministic dynamical system in a quenched random environment. We show,
incorporating results obtained from numerical simulations, that the density
of open paths in any finite box tends to 0 as the box size tends to
infinity, for any mirror probability.

Joint work with David Sanders, available at http://arxiv.org/pdf/1406.4796v1.pdf [arxiv.org]

Joint work with David Sanders, available at http://arxiv.org/pdf/1406.4796v1.pdf [arxiv.org]

2015.02.26 Thursday, 16:15

Exploring the Acyclic Random Graph

Abstract

We consider the Erdos-Renyi graph G(n,p), conditioned to contain no cycles. We use results of Britikov and Luczak to show an Aldous-type limit for the depth-first search within the same critical window as in the classical case, to a limiting process with Brownian excursions.

2015.02.12 Thursday, 16:15

Non-Liouville groups with return probability exponent at most 1/2

Abstract

2015.02.05 Thursday, 16:15