There will be several short talk sessions, during which participants could present their works. Talks will be restricted to 10/15 minutes + 5 minutes for questions. Both a (white)board and a slide talk is possible.
If you still wish to submit a title and an abstract for your talk, fill out the form at the bottom of the list.
Schedule:
Titles and abstracts:
| Sandra Kliem | The one-dimensional KPP-equation driven by space-time white noise | The one-dimensional KPP-equation driven by space-time white noise,
\[ \partial_t u = \partial_{xx} u + \theta u – u^2 + u^{\frac{1}{2}} dW, \qquad t>0, x \in \mathbb{R}, \theta>0, \qquad \qquad u(0,x) = u_0(x) \geq 0 \] is a stochastic partial differential equation (SPDE) that exhibits a phase transition for initial non-negative finite-mass conditions. Solutions to this SPDE arise for instance as (weak) limits of approximate densities of occupied sites in rescaled one-dimensional long range contact processes. If $\theta$ is below a critical value $\theta_c$, solutions die out to $0$ in finite time, almost surely. Above this critical value, the probability of (global) survival is strictly positive. Let $\theta>\theta_c$, then there exist stochastic wavelike solutions which travel with non-negative linear speed. For initial conditions that are ‘’uniformly distributed in space’’, the corresponding solutions are all in the domain of attraction of a unique non-zero stationary distribution. In my talk, I will introduce the model in question and give an overview of existing results, open questions and techniques involved in its analysis. |
| Hugo Panzo | Scaled penalization of Brownian motion with drift and the Brownian ascent | In their study of Brownian penalizations by functions of the endpoint and running maximum, Roynette-Vallois-Yor considered a two-parameter model that exhibited three distinct phases corresponding to three regions of the parameter plane. We extend their results by considering a scaled version of this model and show the existence of three additional “critical” phases, one of which is Brownian motion conditioned to end at its running maximum, the so-called Brownian ascent. |
| Andreas Sojmark | A McKean–Vlasov Equation with Positive Feedback Effects | I will present a McKean–Vlasov problem with a positive feedback effect related to the hitting time of a barrier. This problem arises naturally as a mean field limit when modelling the “spiking” of neurons or the contagious impact of defaults in mathematical finance. For the main part of the talk, I will discuss some difficulties concerning the well-posedness of the problem and then I will outline recent results about short-time uniqueness. |
| Lukas Schoug | An imaginary geometry approach to boundary correlation estimates | In the theory of Schramm-Loewner evolution (SLE) one is often interested in the geometric properties of the curves, and the coupling of SLE and the Gaussian free field (GFF), in which the flow lines of the GFF are variants of SLE curves, gives us new ways to approach these problems. In a recent work, we have investigated a boundary multifractal spectrum of SLE$_\kappa(\rho)$ curves, using the aforementioned coupling, and the goal of this talk is to describe one of the key steps in this analysis: how to use a good one-point estimate to find a good two-point estimate. |
| Sara Mazzonetto | Skew Brownian motion: explicit representation of their transition densities and exact simulation | In this talk we discuss an explicit representation of the transition density of Brownian dynamics undergoing their motion through semipermeable and semireflecting barriers, called skewed Brownian motions.
We mention the applications of the result in the context of the exact simulation of related Brownian diffusions with coefficients admitting jumps. |
| Mikolaj Kasprzak | Diffusion approximations via Stein’s method and time changes | We extend the ideas of (Barbour 1990) and use Stein’s method to obtain a bound on the distance between a scaled time-changed random walk and a time-changed Brownian Motion. We then apply this result to bound the distance between a time-changed compensated scaled Poisson process and a time-changed Brownian Motion. This allows us to bound the distance between a process whose dynamics resemble those of the Moran model with mutation and a process whose dynamics resemble those of the Wright-Fisher diffusion with mutation upon noting that the former may be expressed as a difference of two time-changed Poisson processes and the diffusive part of the latter may be expressed as a time-changed Brownian Motion. The method is applicable to a much wider class of examples satisfying the Stroock-Varadhan theory of diffusion approximation. |
| Ahmed Fadili | Functional convex order for diffusions and their approximation schemes. | We will present some results and open questions about monotony in convex order (with respect to volatility) of solutions of stochastic differential equations, with and without reflection, McKean stochastic differential equations, and Forward Backward stochastic differential equations, and we will study some approximation schemes that preserve this property ( Euler-Maruyama scheme, penalization approximation of a reflected stochastic differential equation, interacting particle systems for McKean equation,…). |
| Franck Maunoury | Infinite divisibility conditions for permanental and multivariate negative binomial distributions | We consider permanental and multivariate negative binomial distributions.
We give simple necessary and sufficient conditions on their kernel, for infinite divisibility, without symmetry hypothesis. When they are not infinitely divisible, we also exhibit some “new†classes of such distributions with non-symmetric kernel. |
| Carlo Bellingeri | Stochastic heat equation and regularity structures | Considered one of the simplest example of stochastic PDE, the additive stochastic heat equation (SHE) may be seen as the dynamical version of Brownian motion or continuous Gaussian free field in dimension 1 or 2. However, compared to these two probabilistic objects, very few tools are knew to study the trajectories of (SHE). In this talk we will simply sketch how the recent theory of regularity structures can contribute to this issue. |
| Anton Klimovsky | Complex-valued random energy models | Phase-transitions are closely related with the distribution of complex-plane zeros of partition functions (cf., Lee-Yang theory). Sums of complex exponentials are at the core of the quantum physics formalism. Finally, striking relationships of the sums of complex random log-correlated exponentials (= complex multiplicative chaos) with characteristic polynomials of random matrices, and the Riemann zeta function were conjectured by Fyodorov et al. All this warrants studies of disordered systems with complex-valued energies. We review our results on several paradigmatic models of range-free disordered systems: complex-valued random energy model (REM), generalized REM (GREM) and branching Brownian motion (BBM) energy models. This is based on joint works with Zakhar Kabluchko and Lisa Hartung. |
| Adrien Barrasso | BSDEs and decoupled mild solutions of (possibly singular, integro or path-dependent) PDEs | The talk will introduce the notion of Decoupled mild solution for a (possibly singular, integro or path-dependent) PDE. It will then present how Backward Stochastic Diffetential equations permit to prove existance and uniqueness of such a solution under mild assumptions. |
| Martin Friesen | The Boltzmann-Enskog process for hard and soft potentials | The time evolution of a gas in the vacuum is classically described by a probability density obtained from the Boltzmann equation. In this work we consider a delocalized version of the Boltzmann equation, i.e. we study the Enskog equation for physical collision kernels including hard and soft potentials. We show that any reasonable measure solution to the Enskog equation can be represented as the one-dimensional distribution of a weak solution to a mean-field type stochastic differential equation with jumps. In the main part of this work we develop, based on a particle approximation of binary collisions, an existence theory for the latter equation. |
| Tal Orenshtein | Critical wetting models in (1+1) dimensions | We will discuss wetting models in (1+1) dimensions pinned to a strip. These are polymer models for which the asymptotic behavior is governed by an interplay between a local effect (pinning) and a global one (entropic repulsion). The standard case, for which the strip size is zero, is completely solved and exhibits a sharp localization-delocalization transition (AKA the wetting transition). In particular, the asymptotic behavior is drastically different in the sub-critical, the super critical and the critical phases. Phase transition results are available also in the case where the strip size is fixed and the pinning function is constant and space homogeneous. We will focus on the strip model at criticality with shrinking strip size. This is a joint work in progress with Jean-Dominique Deuschel. |
| Benedikt Jahnel | Gibbsian representation for point processes via hyperedge potentials | We consider marked point processes on the d-dimensional euclidean space, defined in terms of a quasilocal specification based on marked Poisson point processes. We investigate the possibility of constructing uniformly absolutely convergent Hamiltonians in terms of hyperedge potentials in the sense of Georgii and Dereudre. These potentials are natural generalizations of physical multibody potentials which are useful in models of stochastic geometry. With this we draw a link between the abstract theory of point processes in infinite volume, the study of measures under transformations, and statistical mechanics of systems of point particles. |
| Henri Elad Altman | Integration by Parts Formulae for the Laws of Bessel Bridges, and Stochastic PDEs with Reflection | In a series of papers of the early 2000s, L. Zambotti introduced a family of parabolic stochastic PDEs with reflection at the origin parametrized by a number d ≥ 3, the solutions of which exhibit a rich behavior reminiscent of the Bessel processes. In particular, these processes are nonnegative and continuous, and their unique invariant measure corresponds to the law of the Bessel bridge of dimension d on [0,1]. In addition, Zambotti established integration by parts fomulae for these laws on the set of nonnegative continuous paths, and deduced interesting properties for the corresponding dynamics. However, for a long time, an extension of these constructions and results for all d > 0 remained open.
In this talk, I will present integration by parts formulae for the laws of Bessel bridges of all positive dimension. I will show how the structure of these formulae enables one to conjecture the shape of the stochastic PDEs that might have these laws as their invariant measure, when the dimension is smaller than 3. |
| Renan Gross | If you squint hard enough, Gibbs distributions behave like mixtures of product measures | Gibbs distributions are everywhere, whether you’re Ising-modeling a magnet or fitting an exponential random graph to your social network. Alas, explicitly solving Gibbs distributions can sometimes be a bit hard. In this talk, we’ll discuss a mean-field condition on the Hamiltonian and how this condition decomposes the distribution into a mixture of product measures. These product measures satisfy a vector equation which, if solved, can reveal some of the structure underlying the distribution (e.g symmetry breaking in graphs with a small number of triangles). |
| Sung-Soo Byun | Coulomb gas formalism for the annulus SLE partition function | In this talk, I will present certain implementations of conformal field theory (CFT) in a doubly connected domain. The statistical fields in these implementations are generated by central charge modifications of the continuum Gaussian free field with excursion reflected/Dirichlet boundary conditions.
After outlining the relation between CFT and Schramm Loewner evolution (SLE) theory, I will explain how to apply the method of screening to find explicit solutions of the partial differential equations for the annulus SLE partition functions introduced by Lawler and Zhan. This is based on joint work with Nam-Gyu Kang and Hee-Joon Tak. |
| Marco Furlan | Weak universality for a class of 3d stochastic reaction-diffusion models | Recently M. Hairer and W. Xu (ArXiv: 1601.05138) obtained a convergence result for a class of reaction-diffusion models with stochastic forcing term. Using regularity structures they showed that for a Gaussian forcing term converging to the white noise, and a small (compared to the noise) reaction term which is an odd polynomial, the family converges to the $\Phi^4_3$ model.
In my talk I will show how to extend this result to more general reaction terms (with only a finite number of derivatives and exponential growth), using Malliavin calculus to bound enhanced noise terms in a paracontrolled distributions setting. The result was obtained in a joint work with M. Gubinelli (ArXiv: 1708.03118). |
| Patrick Poschke | Anomalous transport in the eddy lattice flow and the cat’s eye flow | In this talk I will present recent results about the influence of small thermal noise (i.e. large Peclet numbers) on two-dimensional flows. The talk will mainly focus on the analytical and extensive numerical results of a family of flows called “cat’s eye flow”, showing all kinds of anomalous diffusion (ranging from subdiffusive to super-ballistic depending on time and on the parameter “A” of the flow). By tuning A, one changes from a pure shear flow (A=1), via flows possessing nearly elliptic eddies in the shape of cat’s eyes next to nearly sinusoidal jets for A in (0,1), to the special case of the eddy lattice flow (A=0), i.e. an infinite 2D lattice of quadratic cells each containing an eddy. |
| Henri Elad Altman | Integration by Parts Formulae for the Laws of Bessel Bridges, and Stochastic PDEs with Reflection | In a series of papers of the early 2000s, L. Zambotti introduced a family of parabolic stochastic PDEs with reflection at the origin parametrized by a number d ≥ 3, the solutions of which exhibit a rich behavior reminiscent of the Bessel processes. In particular, these processes are nonnegative and continuous, and their unique invariant measure corresponds to the law of the Bessel bridge of dimension d on [0,1]. In addition, Zambotti established integration by parts fomulae for these laws on the set of nonnegative continuous paths, and deduced interesting properties for the corresponding dynamics. However, for a long time, an extension of these constructions and results for all d > 0 remained open. In this talk, I will present integration by parts formulae for the laws of Bessel bridges of all positive dimension. I will show how the structure of these formulae enables one to conjecture the shape of the stochastic PDEs that might have these laws as their invariant measure, when the dimension is smaller than 3. |
| Adrien Barrasso | BSDEs and decoupled mild solutions of (possibly singular, integro or path-dependent) PDEs | The talk will introduce the notion of Decoupled mild solution for a (possibly singular, integro or path-dependent) PDE. It will then present how Backward Stochastic Differential equations permit to prove existence and uniqueness of such a solution under mild assumptions. |
| Alexander Nerlich | The strong Law of large Numbers and the central limit Theorem for abstract Cauchy Problems driven by random Measures |
In this talk, we establish the SLLN as well as the CLT for a class of vector-valued stochastic processes X : [0,∞) × Ω → V which arise as solutions of the stochastic differential inclusion η(t,z)N Θ (dt ⊗ z) ∈ dX(t) + AX(t)dt, (ACPRM) where (V,||·|| V ) is a separable Banach space, A is a multi-valued, densely defined, m-accretive operator acting on V and N Θ is the counting measure induced by a point process Θ. The SLLN and the CLT will be proven not only for real-valued, but also for vector-valued functionals and the applicability of these theoretical results to the (weighted) p-Laplacian evolution equation (for ”small” p) will be demonstrated. Moreover, the class of functionals is sufficiently large to prove these results for X itself and for certain norms which are stronger than || · || V . Particularly, in the p-Laplacian case our results yield the SLLN and the CLT for the solution itself and all L q -norms of the process, where q ∈ [1,∞). The key assumption needed to achieve this, is that the nonlinear semigroup arising from the multi-valued operator A extincts in finite time. Of course, some distributional assumptions regarding the noise are also necessary. |
Please submit your short-talk information below. The deadline for talk information submissions is 10/12/2017.