Consider an N -dimensional Markov chain obtained from N onedimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller Markov process. The dynamical correlation functions of the limit process are determinantal with an explicit correlation kernel. The key idea is to identify rand...

In this paper we extend the notion of “filtration-consistent nonlinear expectation” (or “Fconsistent nonlinear expectation”) to the case when it is allowed to be dominated by a gexpectation that may have a quadratic growth. We show that for such a nonlinear expectation many fundamental properties of a martingale can still make sense, including the Doob-Meyer type decomposition theorem and the o...

In this notes we shall describe the relation of a certain class of simple random curves arising in 2D statistical mechanics models in the scaling limit, which can be described dynamically by Stochastic Lœwner Evolutions (SLE), and the equivalent Renormalisation Group (RG) theoretic interpretation in Conformal Field Theory, as a fixed point of the RG flow. Further, we shall recall the relation o...

We develop a general dynamical model as a framework for possible causal interpretation. We first state a criterion of local independence in terms of measurability of processes involved in the Doob-Meyer decomposition of stochastic processes, as in Aalen (1987); then we define direct and indirect influence. We propose a definition of causal influence using the concepts of “physical system”. This...

We consider continuous-state branching (CB) processes which become extinct (i.e., hit 0) with positive probability. We characterize all the quasi-stationary distributions (QSD) for the CB-process as a stochastically monotone family indexed by a real number. We prove that the minimal element of this family is the so-called Yaglom quasi-stationary distribution, that is, the limit of one-dimension...

The Schramm-Loewner evolution (SLEκ) is a candidate for the scaling limit of random curves arising in two-dimensional critical phenomena. When κ < 8, an instance of SLEκ is a random planar curve with almost sure Hausdorff dimension d = 1 + κ/8 < 2. This curve is conventionally parametrized by its half plane capacity, rather than by any measure of its d-dimensional volume. For κ < 8, we use a Do...

Content analysis of 122 social psychology textbooks confirmed that displaced aggression received a surge of attention immediately following J. Dollard, L. W. Doob, N. E. Miller, O. H. Mowrer, and R. R. Sears (1939), but subsequent interest sharply declined. Contemporary texts give it little attention. By contrast, meta-analysis of the experimental literature confirms that it is a robust effect ...

where (x(£),x(0) = 0,0fktfíl\ is a Brownian motion process. Equation (0.1) has been studied by S. Bernstein [l], J. L. Doob [5] and others [2], [ 10]. In general, the solution given here is different from that given by these authors. Equation (0.1) is almost purely formal since the derivative dx/dt fails to exist with probability one. In [2], [5], [ 10], the stochastic integral of K. Ito [7], [...

We develop a new method to obtain stochastic characterizations of Yang–Mills elds. Our main tool is the Itô-equation for the stochastic parallel transport. We estimate the drift terms in a small ball of radius and nd that for a general connection the average rotation is of order 3 but that for a Yang–Mills connections the average rotation is of order . Using a Doob h-transform we give a new pro...