692 research outputs found
Disconnection and Entropic Repulsion for the Harmonic Crystal with Random Conductances
No full textWe study level-set percolation for the harmonic crystal on Zd, d≥ 3 , with uniformly elliptic random conductances. We prove that this model undergoes a non-trivial phase transition at a critical level that is almost surely constant under the environment measure. Moreover, we study the disconnection event that the level-set of this field below a level α disconnects the discrete blow-up of a compact set A⊆ Rd from the boundary of an enclosing box. We obtain quenched asymptotic upper and lower bounds on its probability in terms of the homogenized capacity of A, utilizing results from Neukamm, Schäffner and Schlömerkemper (SIAM J Math Anal 49(3):1761–1809, 2017). Furthermore, we give upper bounds on the probability that a local average of the field deviates from some profile function depending on A, when disconnection occurs. The upper and lower bounds concerning disconnection that we derive are plausibly matching at leading order. In this case, this work shows that conditioning on disconnection leads to an entropic push-down of the field. The results in this article generalize the findings of Nitzschner (Electron J Probab 23:105, 2018) and Chiarini and Nitzschner (Probab Theory Relat Fields 177(1–2):525–575, 2020) which treat the case of constant conductances. Our proofs involve novel “solidification estimates” for random walks, which are similar in nature to the corresponding estimates for Brownian motion derived by Nitzschner and Sznitman (J Eur Math Soc. 22:2629–2672, 2020)
Phase transition for level-set percolation of the membrane model in dimensions
No full textWe consider level-set percolation for the Gaussian membrane model on
, with , and establish that as
varies, a non-trivial percolation phase transition for the level-set above
level occurs at some finite critical level , which we show to be
positive in high dimensions. Along , two further natural critical
levels and are introduced, and we establish that
, in all
dimensions. For , we find that the connectivity function of
the level-set above admits stretched exponential decay, whereas for , chemical distances in the (unique) infinite cluster of the
level-set are shown to be comparable to the Euclidean distance, by verifying
conditions identified by Drewitz, R\'ath and Sapozhnikov, see arXiv:1212.2885,
for general correlated percolation models. As a pivotal tool to study its
level-set, we prove novel decoupling inequalities for the membrane model.Comment: 29 pages, 1 figure, to appear in Journal of Statistical Physic
Entropic repulsion for the occupation-time field of random interlacements conditioned on disconnection
No full textWe investigate percolation of the vacant set of random interlacements on
, , in the strongly percolative regime. We consider the
event that the interlacement set at level disconnects the discrete blow-up
of a compact set from the boundary of an enclosing
box. We derive asymptotic large deviation upper bounds on the probability that
the local averages of the occupation times deviate from a specific function
depending on the harmonic potential of , when disconnection occurs. If
certain critical levels coincide, which is plausible but open at the moment,
these bounds imply that conditionally on disconnection, the occupation-time
profile undergoes an entropic push governed by a specific function depending on
. Similar entropic repulsion phenomena conditioned on disconnection by
level-sets of the discrete Gaussian free field on , ,
have been obtained by the authors in arxiv:1808.09947. Our proofs rely
crucially on the `solidification estimates' developed in arXiv:1706.07229 by
A.-S. Sznitman and the second author.Comment: 35 pages, 2 figures, accepted in the Annals of Probabilit
Entropic repulsion for the Gaussian free field conditioned on disconnection by level-sets
No full textWe investigate level-set percolation of the discrete Gaussian free field on
, , in the strongly percolative regime. We consider the
event that the level-set of the Gaussian free field below a level
disconnects the discrete blow-up of a compact set from the boundary of an
enclosing box. We derive asymptotic large deviation upper bounds on the
probability that the local averages of the Gaussian free field deviate from a
specific multiple of the harmonic potential of , when disconnection occurs.
These bounds, combined with the findings of the recent article [12], show that
conditionally on disconnection, the Gaussian free field experiences an entropic
push-down proportional to the harmonic potential of . In particular, due to
the slow decay of correlations, the disconnection event affects the field on
the whole lattice. Furthermore, we provide a certain 'profile' description for
the field in the presence of disconnection. We show that while on a macroscopic
scale the field is pinned around a level proportional to the harmonic potential
of , it locally retains the structure of a Gaussian free field shifted by a
constant value. Our proofs rely crucially on the 'solidification estimates'
developed in arXiv:1706.07229 by A.-S. Sznitman and the second author.Comment: Accepted in Probability Theory and Related Field
Assessment of glycosylation patterns in human chorionic gonadotropin drug products
No full textthesis author: Maximilian LebedeMasterarbeit University of Salzburg 2019Abstract in deutscher und englischer Sprach
Axiale Drehmomentenmessung in der Einschneckenextrusion
No full textAuthor DI Maximilian Prechtl BScAbweichender Titel laut Übersetzung der Verfasserin/des VerfassersDissertation Johannes Kepler Universität Linz 2022Arbeit gesperr
In defense of St. Maximilian the Theologian
No full textThe author disagrees with opinions of certain theologians which refuse St. Maximilian the title of Theologian. In his thinking coming from the concept of theology being understood from the Slovian root word − Bogo-słowije, which is equal to the Greek Theo-logia; in analogy – theology means: God’s Word Bogosłow (gr. Theologos). On the basis of Fr. Kolbe’s writings, the author proves his point that not only can St. Maximilian be counted as a theologian, but also among the elite group of the Three Theologians. A Theologian is not only a person „learned in Scriptures”, but a mystic, a person who comes to know God through contemplation, which does not come without the intellect’s part also. The main „instrument” of knowledge of God is prayer. Prayer brings a person to divinization. With divinization (sanctification), full human knowledge and being are realized. A person reaches his/her fullness – completeness in one’s ability; „touches” the theological reality. It is the most intimate sphere for human knowledge as well as human existence. St. Maximilian, similar to the great Theologians − St.John Theologian, author of „Tractate” about the Logos (J 1, 1–14) plus the well-known followers: St. Gregory Nazian, St. Simon the New Theologian – who belong to this very „category” of Theologians. Also his theology is based on becoming holy = divinization (sanctification). A Theologian is a person who is prayerful, contemplating the vision of God, and not just a scholar who aims for a university position and teaching career. St. Maximilian was such a person: he was a Theologian in the fullest sense of the meaning
Synthesis and evaluation of half-sandwich manganese complexes in [2+2+2] cycloaddition reactions
No full textAuthor Maximilian BayerMasterarbeit Johannes Kepler Universität Linz 2025Arbeit nach Ablauf der Sperre auf den öffentlichen PCs in den Bibliotheken der JKU+Medizin abrufba
Structural analysis and optimization of a tethered swept wing for airborne wind energy generation (vol 23, pg 1006, 2020): Structural analysis and optimization of a tethered swept wing for airborne wind energy generation (Wind Energy, (2020), 23, 4, (1006-1025), 10.1002/we.2469)
No full textIn Candade et al,1 the authors would like to correct the affiliations of Maximilian Ranneberg2 and Roland Schmehl1.Wind Energ
Absence of weak disorder for directed polymers on supercritical percolation clusters
No full textWe study the directed polymer model on infinite clusters of supercritical Bernoulli percolation containing the origin in dimensions d≥3, and prove that for almost every realization of the cluster and every strictly positive value of the inverse temperature, the polymer is in a strong disorder phase, answering a question from Cosco, Seroussi, and Zeitouni, see arXiv:2010.09503
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