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pro vyhledávání: '"van Zuijlen, Willem"'
We investigate a model of continuous-time simple random walk paths in $\mathbb{Z}^d$ undergoing two competing interactions: an attractive one towards the large values of a random potential, and a self-repellent one in the spirit of the well-known wea
Externí odkaz:
http://arxiv.org/abs/2306.03788
Autor:
Matsuda, Toyomu, van Zuijlen, Willem
We construct random Schr\"odinger operators, called Anderson Hamiltonians, with Dirichlet and Neumann boundary conditions for a fairly general class of singular random potentials on bounded domains. Furthermore, we construct the integrated density of
Externí odkaz:
http://arxiv.org/abs/2211.01199
We consider the parabolic Anderson model (PAM) $\partial_t u = \frac12 \Delta u + \xi u$ in $\mathbb R^2$ with a Gaussian (space) white-noise potential $\xi$. We prove that the almost-sure large-time asymptotic behaviour of the total mass at time $t$
Externí odkaz:
http://arxiv.org/abs/2009.11611
We consider the stochastic differential equation on $\mathbb{R}^d$ given by $$ \, \mathrm{d}X_t = b(t,X_t) \, \mathrm{d}t + \, \mathrm{d} B_t, $$ where $B$ is a Brownian motion and $b$ is considered to be a distribution of regularity $ > -\frac12$. W
Externí odkaz:
http://arxiv.org/abs/2009.10786
Autor:
Chouk, Khalil, van Zuijlen, Willem
In this paper we consider the Anderson Hamiltonian with white noise potential on the box $[0,L]^2$ with Dirichlet boundary conditions. We show that all the eigenvalues divided by $\log L$ converge as $L\rightarrow \infty$ almost surely to the same de
Externí odkaz:
http://arxiv.org/abs/1907.01352
We study the loss, recovery, and preservation of differentiability of time-dependent large deviation rate functions. This study is motivated by mean-field Gibbs-non-Gibbs transitions. The gradient of the rate-function evolves according to a Hamiltoni
Externí odkaz:
http://arxiv.org/abs/1711.03489
Autor:
van Zuijlen, Willem
We study product regular conditional probabilities under measures of two coordinates with respect to the second coordinate that are weakly continuous on the support of the marginal of the second coordinate. Assuming that there exists a sequence of pr
Externí odkaz:
http://arxiv.org/abs/1605.05192
Autor:
van Rooij, Arnoud, van Zuijlen, Willem
We present a natural way to cover an Archimedean directed ordered vector space $E$ by Banach spaces and extend the notion of Bochner integrability to functions with values in $E$. The resulting set of integrable functions is an Archimedean directed o
Externí odkaz:
http://arxiv.org/abs/1604.06341
Autor:
van Rooij, Arnoud, van Zuijlen, Willem
We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure space leads to
Externí odkaz:
http://arxiv.org/abs/1505.05997
Publikováno v:
Stochastic Processes and their Applications, Volume 125, Issue 1, January 2015, Pages 371-400
We consider a system of real-valued spins interacting with each other through a mean-field Hamiltonian that depends on the empirical magnetization of the spins via a general potential. The system is subjected to a stochastic dynamics where the spins
Externí odkaz:
http://arxiv.org/abs/1312.3438