This term, all seminars take place Thursdays at 2pm, room MS.04 (Zeeman Building), unless indicated otherwise.



Schedule for

Sayan Banerjee, 20.02.2014

Seminars

11.01.2018 Agelos Georgakopoulos (University of Warwick)
Analytic functions in bond percolation
We consider Bernoulli bond percolation on various graphs/groups and prove that certain functions are analytic in the percolation parameter p. Joint work with C. Panagiotis.
18.01.2018 Rangel Baldasso (Bar-Ilan University)
Noise sensitivity for Voronoi percolation
Noise sensitivity is a concept that measures if the outcome of Boolean function can be predicted when one is given its value for a perturbation of the configuration. A sequence of functions is noise sensitive when this is asymptotically not possible. A non-trivial example of a sequence that is noise sensitive is the crossing functions in critical two-dimensional Bernoulli percolation. In this setting, noise sensitivity can be understood via the study of randomized algorithms. Together with a discretization argument, these techniques can be extended to the continuum setting. In this talk, we prove noise sensitivity for critical Voronoi percolation in dimension two, and derive some consequences of it.
Based on a joint work with D. Ahlberg.

Contact: Elisabetta
25.01.2018 Peter Mühlbacher (IST Vienna)
Bounds on the norm of Wigner-type random matrices
We consider a Wigner-type ensemble, i.e. large hermitian NxN random matrices H=H^* with centered independent entries and with a general matrix of variances S_xy= E|H_xy|^2. The norm of H is asymptotically given by the maximum of the support of the self-consistent density of states. We establish a bound on this maximum in terms of norms of powers of S that substantially improves the earlier bound 2| S|^{1/2}_infty. The key element of the proof is an effective Markov chain approximation for the contributions of the weighted Dyck paths appearing in the iterative solution of the corresponding Dyson equation.

SPECIAL TIME AND LOCATION: 11-12 in B1.12

Contact: Daniel
25.01.2018 Cesare Nardini (CEA Saclay)
Two many-body phenomena in active matter: A minimal model approach
Each component of an active system is able to extract energy from the environment and transform it into motion. I will discuss two cases where active systems show qualitative different physics with respect to equilibrium ones, arising when the fluid in which particles swim is either negligible or has a dominant effect.
In the first part, I will focus on incomplete phase separation, the fact that repulsive particles tend to phase separate when they are active. Due to the non-equilibrium nature of the problem, however, this `phase separation’ is often incomplete: either it is arrested to a finite-size clusters phase or the liquid region supports the continuous nucleation of vapour bubbles in its interior. I will discuss how these phenomena can be captured by extending classical phi^4 theory for equilibrium phase separation to include active terms. Results are mostly analytical, based on a reanalysis of Ostwald Ripening and Renormalisation Group. Numerics backs our conclusions.
If time allows, in the second part I will focus on predicting the diffusion constant of a passive tracer when immersed in a bacterial suspension. We develop a kinetic theory approach very similar to the one used in the study of plasma and numerical simulations to show that, differently to what previously assumed in literature, `a bacteria never swim alone’: correlations matter even at very low densities.

Contact: Tobias
01.02.2018 Cristian Giardina (Modena)
Boundary driven 2D Ising model
I will discuss properties of the non-equilibrium stationary state of the two-dimensional Ising model coupled to magnetization reservoirs. When the boundaries impose magnetization values corresponding to opposite phases, a free boundary problem (of Stefan type) describes the evolution of the interface in the hydrodynamic limit. I will argue that the stationary solutions in the metastable or unstable phase may sustain a current that is going uphill, i.e. from the reservoir with lower magnetization to the one with larger magnetization.
Contact: Stefan G
08.02.2018 Daisuke Shiraishi (Kyoto University)
Geometry of Brownian motion
In this talk, we will consider the nature of self-intersections of the Brownian motion in R^d. It is well-known that the Brownian motion is a simple path if d > 3, while it has loops when d =1,2,3. What are loops of the Brownian motion? How are those loops distributed in space? These are questions we want to address. In the talk, we give an explicit representation of such loops for d=1,2,3 by establishing a decomposition of the Brownian path into independent simple path and a set of loops. It turns out that the simple path and the set of loops can be described by the scaling limit of the loop-erased random walk and a Poisson point process on a path space, respectively. We will also explain a relation between our results and Ito’s excursion theory. This is joint work with Artem Sapozhnikov (University of Leipzig).
Contact: David
15.02.2018


22.02.2018 Tyler Helmuth (University of Bristol)
Recurrence of the vertex-reinforced jump process in two dimensions
The vertex-reinforced jump process (VRJP) is a linearly reinforced random walk in continuous time. Roughly speaking, the VRJP prefers to jump to vertices it has visited in the past. The model contains a parameter which controls the strength of the reinforcement.
Sabot and Tarres have shown that the VRJP is related to the H22 supersymmetric hyperbolic spin model, a model that originated in the study of random band matrices. By making use of results for the H22 model they were able to prove recurrence of the VRJP for strong reinforcement in all dimensions. I will present a new and direct connection between the VRJP and hyperbolic spin models (both supersymmetric and classical), and show how this connection can be used to prove that the VRJP is recurrent in two dimensions for any reinforcement strength.
Based on joint work with R. Bauerschmidt and A. Swann.

Contact: Daniel
01.03.2018 Stephen Muirhead (King s College)
TBA

Contact: Daniel
08.03.2018 Christina Goldschmidt (University of Oxford)
TBA

Contact: Daniel
15.03.2018