Zobrazeno 1 - 10
of 216
pro vyhledávání: '"Betz, Volker"'
In [Muhl2019], Peter M\"uhlbacher showed that in the random loop model without loop weights, a loop phase transition (assuming it exists) cannot occur at the same parameter as the percolation phase transition of the occupied edges. In this work, we g
Externí odkaz:
http://arxiv.org/abs/2408.00648
We study Brownian paths perturbed by semibounded pair potentials and prove upper bounds on the mean square displacement. As a technical tool we derive infinite dimensional versions of key inequalities that were first used in [Sellke; arXiv:2212.14023
Externí odkaz:
http://arxiv.org/abs/2312.02709
We show that a properly scaled stretched long Brownian chain converges to a two-parametric stochastic process, given by the sum of an explicit deterministic continuous function and the solution of the stochastic heat equation with zero boundary condi
Externí odkaz:
http://arxiv.org/abs/2305.03541
We consider a biased nearest-neighbor random walk on $\Z$ which at each step is trapped for some random time with random, site-dependent mean. We derive a simple formula for the speed function in terms of the model parameters.
Comment: 10 pages,
Comment: 10 pages,
Externí odkaz:
http://arxiv.org/abs/2209.00241
Autor:
Betz, Volker, Polzer, Steffen
We show that the effective mass of the Fr\"ohlich Polaron is bounded below by $c\alpha^{2/5}$ for some constant $c>0$ and for all coupling constants $\alpha$. The proof uses the point process representation of the path measure of the Fr\"ohlich Polar
Externí odkaz:
http://arxiv.org/abs/2201.06445
Autor:
Betz, Volker, Polzer, Steffen
The application of the Feynman-Kac formula to Polaron models of quantum theory leads to the path measure of Brownian motion perturbed by a pair potential that is translation invariant both in space and time. An important problem in this context is th
Externí odkaz:
http://arxiv.org/abs/2106.06447
We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise potential $U$, with one end of the chain fixed and the other end pulled away, in the limit of slow pulling speed and small Brownian noise. We study t
Externí odkaz:
http://arxiv.org/abs/2010.07706
We consider Ewens random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$ and to study the asymptotic behaviour as $n\to\infty$. We obtain very precise information on the joint distribution of the lengths
Externí odkaz:
http://arxiv.org/abs/2004.09904
We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise quadratic potential, with one end of the chain fixed and the other end pulled away at slow speed, in the limit of slow speed and small Brownian noise
Externí odkaz:
http://arxiv.org/abs/1912.05168
We investigate the random loop model on the $d$-ary tree. For $d \geq 3$, we establish a (locally) sharp phase transition for the existence of infinite loops. Moreover, we derive rigorous bounds that in principle allow to determine the value of the c
Externí odkaz:
http://arxiv.org/abs/1812.03937