69 research outputs found
On L-infinity morphisms of cyclic chains
Recently the first two authors constructed an L-infinity morphism using the
S^1-equivariant version of the Poisson Sigma Model (PSM). Its role in
deformation quantization was not entirely clear. We give here a "good"
interpretation and show that the resulting formality statement is equivalent to
formality on cyclic chains as conjectured by Tsygan and proved recently by
several authors.Comment: 11 page
From Maximum of Intervisit Times to Starving Random Walks
Very recently, a fundamental observable has been introduced and analyzed to
quantify the exploration of random walks: the time required for a
random walk to find a site that it never visited previously, when the walk has
already visited distinct sites. Here, we tackle the natural issue of the
statistics of , the longest duration out of .
This problem belongs to the active field of extreme value statistics, with the
difficulty that the random variables are both correlated and
non-identically distributed. Beyond this fundamental aspect, we show that the
asymptotic determination of the statistics of finds explicit applications
in foraging theory and allows us to solve the open -dimensional starving
random walk problem, in which each site of a lattice initially contains one
food unit, consumed upon visit by the random walker, which can travel
steps without food before starving. Processes of diverse nature,
including regular diffusion, anomalous diffusion, and diffusion in disordered
media and fractals, share common properties within the same universality
classes
Formality theorems for Hochschild complexes and their applications
We give a popular introduction to formality theorems for Hochschild complexes
and their applications. We review some of the recent results and prove that the
truncated Hochschild cochain complex of a polynomial algebra is non-formal.Comment: Submitted to proceedings of Poisson 200
Survival probability of stochastic processes beyond persistence exponents
For many stochastic processes, the probability of not-having reached a
target in unbounded space up to time follows a slow algebraic decay at long
times, . This is typically the case of symmetric compact
(i.e. recurrent) random walks. While the persistence exponent has been
studied at length, the prefactor , which is quantitatively essential,
remains poorly characterized, especially for non-Markovian processes. Here we
derive explicit expressions for for a compact random walk in unbounded
space by establishing an analytic relation with the mean first-passage time of
the same random walk in a large confining volume. Our analytical results for
are in good agreement with numerical simulations, even for strongly
correlated processes such as Fractional Brownian Motion, and thus provide a
refined understanding of the statistics of longest first-passage events in
unbounded space
Derived coisotropic structures I: affine case
We define and study coisotropic structures on morphisms of commutative dg
algebras in the context of shifted Poisson geometry, i.e. -algebras.
Roughly speaking, a coisotropic morphism is given by a -algebra acting
on a -algebra. One of our main results is an identification of the space
of such coisotropic structures with the space of Maurer--Cartan elements in a
certain dg Lie algebra of relative polyvector fields. To achieve this goal, we
construct a cofibrant replacement of the operad controlling coisotropic
morphisms by analogy with the Swiss-cheese operad which can be of independent
interest. Finally, we show that morphisms of shifted Poisson algebras are
identified with coisotropic structures on their graph.Comment: 49 pages. v2: many proofs rewritten and the paper is split into two
part
Universal star products
One defines the notion of universal deformation quantization: given any
manifold , any Poisson structure on and any torsionfree linear
connection on , a universal deformation quantization associates to
this data a star product on given by a series of bidifferential
operators whose corresponding tensors are given by universal polynomial
expressions in the Poisson tensor , the curvature tensor and their
covariant iterated derivatives. Such universal deformation quantization exist.
We study their unicity at order 3 in the deformation parameter, computing the
appropriate universal Poisson cohomology.Comment: To appear in Letters in Mathematical Physic
The quantization of the symplectic groupoid of the standard Podles sphere
We give an explicit form of the symplectic groupoid that integrates the
semiclassical standard Podles sphere. We show that Sheu's groupoid, whose
convolution C*-algebra quantizes the sphere, appears as the groupoid of the
Bohr-Sommerfeld leaves of a (singular) real polarization of the symplectic
groupoid. By using a complex polarization we recover the convolution algebra on
the space of polarized sections. We stress the role of the modular class in the
definition of the scalar product in order to get the correct quantum space.Comment: 33 pages; minor correction
Grothendieck-Teichm\"uller and Batalin-Vilkovisky
It is proven that, for any affine supermanifold equipped with a constant
odd symplectic structure, there is a universal action (up to homotopy) of the
Grothendieck-Teichm\"uller Lie algebra on the set of quantum
BV structures (i. e.\ solutions of the quantum master equation) on
Detection of two new RRATs at 111 MHz
A search for pulse signals in a area with declinations of +52\degr <\delta
<+55\degr was carried out on the LPA LPI radio telescope. When processing ten
months of observations recorded in six frequency channels with a channel width
of 415 kHz and a total bandwidth of 2.5 MHz, 22 thousand events were found with
a pronounced dispersion delay of signals over frequency channels, i.e. having
signs of pulsar pulses. It turned out that the found pulses belong to four
known pulsars and two new rotating radio transients (RRATs). An additional
pulse search conducted in 32-channel data with a channel width of 78 kHz
revealed 8 pulses for the transient J0249+52 and 7 pulses for the transient
J0744+55. Periodic radiation of transients was not detected. The analysis of
observations shows that the found RRATs are most likely pulsars with nullings,
where the proportion of nulling is greater than 99.9\%.Comment: published in Astronomy Reports, translated by Yandex translator with
correction of scientific lexis, 5 pages, 2 figures, 1 tabl
Compatibility with cap-products in Tsygan's formality and homological Duflo isomorphism
In this paper we prove, with details and in full generality, that the
isomorphism induced on tangent homology by the Shoikhet-Tsygan formality
-quasi-isomorphism for Hochschild chains is compatible with
cap-products. This is a homological analog of the compatibility with
cup-products of the isomorphism induced on tangent cohomology by Kontsevich
formality -quasi-isomorphism for Hochschild cochains.
As in the cohomological situation our proof relies on a homotopy argument
involving a variant of {\bf Kontsevich eye}. In particular we clarify the
r\^ole played by the {\bf I-cube} introduced in \cite{CR1}.
Since we treat here the case of a most possibly general Maurer-Cartan
element, not forced to be a bidifferential operator, then we take this
opportunity to recall the natural algebraic structures on the pair of
Hochschild cochain and chain complexes of an -algebra. In particular
we prove that they naturally inherit the structure of an -algebra
with an -(bi)module.Comment: The first and second Section on -algebras and modules have
been completely re-written, with new results; partial revision of Section 3;
the proofs in Section 4 and 5 have been re-formulated in a more general
context; we added Section 8 on globalisatio
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