SLEs as boundaries of clusters of Brownian loops

In this research announcement, we show that SLE curves can in fact be viewed as boundaries of certain simple Poissonian percolation clusters: Recall that the Brownian loop-soup (introduced in the paper arxiv:math.PR/0304419 with Greg Lawler) with intensity c defines a Poissonian collection of (simple if one focuses only on the outer boundary) loops in a domain. This random family of (possibly intersecting) loops is conformally invariant (and there are almost surely infinitely many small loops in any sample). We show that there exists a critical value a in (0,1] such that if one colors all the interiors of the loops, the obtained clusters are bounded when ca, one single cluster fills the domain. We prove that for small c, the outer boundaries of the clusters are SLE-type curves where $\kappa \le 4$ and $c$ related by the usual relation $c=(3\kappa-8)(6-\kappa)/2\kappa$ (i.e. c corresponds to the central charge of the model). Conjecturally, the critical value a is equal to one and corresponds to SLE4 loops, so that this should give for any c in (0,1] a construction of a natural countable family of random disjoint SLE$_\kappa$ loops (i.e. $\kappa$ should span $(8/3,4]$), that behaves ``nicely'' under perturbation of the domain. A precise relation between chordal SLE and the loop-soup goes as follows: Consider the sample of a certain restriction measure (i.e. a certain union of Brownian excursions) in a domain, attach to it all the above-described clusters that it intersects. The outer boundary of the obtained set is exactly an SLE$_\kappa$, if the restriction measure exponent is equal to the highest-weight of the corresponding representation with central charge c.Comment: Research anouncement, to appear in C. R. Acad. Sci. Pari

A simple renormalization flow for FK-percolation models

We present a setup that enables to define in a concrete way a renormalization flow for the FK-percolation models from statistical physics (that are closely related to Ising and Potts models). In this setting that is applicable in any dimension of space, one can interpret perturbations of the critical (conjectural) scaling limits in terms of stationary distributions for rather simple Markov processes on spaces of abstract discrete weighted graphs.Comment: 12 pages, to appear in the Jean-Michel Bismut 65th anniversary volum

Formal Specification and Verification of Fully Asynchronous Implementations of the Data Encryption Standard

This paper presents two formal models of the Data Encryption Standard (DES), a first using the international standard LOTOS, and a second using the more recent process calculus LNT. Both models encode the DES in the style of asynchronous circuits, i.e., the data-flow blocks of the DES algorithm are represented by processes communicating via rendezvous. To ensure correctness of the models, several techniques have been applied, including model checking, equivalence checking, and comparing the results produced by a prototype automatically generated from the formal model with those of existing implementations of the DES. The complete code of the models is provided as appendices and also available on the website of the CADP verification toolbox.Comment: In Proceedings MARS 2015, arXiv:1511.0252

The Virtue of Being Underestimated: A Note on Discriminatory Contracts in Hidden Information Models

A standard hidden information model is considered to study the influence of the a priori productivity distribution on the optimal contract. A priori more productive (hazard rate dominant) agents work less, enjoy lower rents, but generate a higher expected surplus.adverse selection, statistical discrimination, stochastic order relation

You Don't Always Get What You Pay For

Consider a principal-agent relationship in which more effort by the agent raises the likelihood of success. Does rewarding success, i.e., paying a bonus, increase effort in this case? I find that bonuses have not only an incentive but also an income effect. Overall, bonuses paid for success may well reduce effort and hence the probability of success. I also identify conditions under which the income effect dominates the incentive effect, and single out the hazard-rate of effort as a crucial determinant of this trade-off.bonus, premium, incentives, income effect, moral hazard

Traits, Imitation and Evolutionary Dynamics

In this article, a modelling framework for the information transmission between agents in an evolutionary game setting is proposed. Agents observe traits which reflect past and present behaviour and success of other agents. If agents imitate more successful agents based on these traits, the resulting dynamics are a multivariate stochastic process. An example for such a process is simulated. The results resemble the replicator dynamics to a remarkable degree. If traits moderately depend on the past, this accelerates convergence of the dynamics towards a stable state. If the dependence is strong, the stable state is not reached.replicator dynamics, imitation, evolution of cooperation, information transmission, simulation