On the spectral gap of Kawasaki dynamics under a mixing condition revisited

2000 ◽  
Vol 41 (3) ◽  
pp. 1391-1423 ◽  
Author(s):  
N. Cancrini ◽  
F. Martinelli
Keyword(s):  
Spectral Gap ◽  
Kawasaki Dynamics ◽  
Mixing Condition

scholarly journals Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian

2021 ◽  
Author(s):  
Jürgen Jost ◽  
Raffaella Mulas ◽  
Florentin Münch
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
Spectral Gap ◽  
Complete Bipartite Graph ◽  
Graph Laplacian ◽  
New Method ◽  
Single Edge ◽  
Largest Eigenvalue ◽  
Complement Graph ◽  
The Largest Eigenvalue

AbstractWe offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least $$\frac{n+1}{n-1}$$ n + 1 n - 1 provided the graph is not complete and that equality is attained if and only if the complement graph is a single edge or a complete bipartite graph with both parts of size $$\frac{n-1}{2}$$ n - 1 2 . With the same method, we also prove a new lower bound to the largest eigenvalue in terms of the minimum vertex degree, provided this is at most $$\frac{n-1}{2}$$ n - 1 2 .

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

scholarly journals Persistence of the spectral gap for the Landau–Pekar equations

2021 ◽  
Vol 111 (1) ◽  
Author(s):  
Dario Feliciangeli ◽  
Simone Rademacher ◽  
Robert Seiringer
Keyword(s):  
Initial Data ◽  
Spectral Gap ◽  
Effective Hamiltonian ◽  
Adiabatic Theorem ◽  
Strongly Coupled

AbstractThe Landau–Pekar equations describe the dynamics of a strongly coupled polaron. Here, we provide a class of initial data for which the associated effective Hamiltonian has a uniform spectral gap for all times. For such initial data, this allows us to extend the results on the adiabatic theorem for the Landau–Pekar equations and their derivation from the Fröhlich model obtained in previous works to larger times.

scholarly journals Nonzero spectral gap in several uniformly spin-2 and hybrid spin-1 and spin-2 AKLT models

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Wenhan Guo ◽  
Nicholas Pomata ◽  
Tzu-Chieh Wei
Keyword(s):  
Spectral Gap

scholarly journals Spectral gap in random bipartite biregular graphs and applications

2021 ◽  
pp. 1-39
Author(s):  
Gerandy Brito ◽  
Ioana Dumitriu ◽  
Kameron Decker Harris
Keyword(s):  
Community Detection ◽  
Adjacency Matrix ◽  
Moment Method ◽  
Coding Theory ◽  
High Probability ◽  
Spectral Gap ◽  
Matrix Completion ◽  
Full Rank ◽  
The Moment ◽  
Deterministic Matrix

Abstract We prove an analogue of Alon’s spectral gap conjecture for random bipartite, biregular graphs. We use the Ihara–Bass formula to connect the non-backtracking spectrum to that of the adjacency matrix, employing the moment method to show there exists a spectral gap for the non-backtracking matrix. A by-product of our main theorem is that random rectangular zero-one matrices with fixed row and column sums are full rank with high probability. Finally, we illustrate applications to community detection, coding theory, and deterministic matrix completion.

Analysis of local velocity gradients in rapid mixer using particle image velocimetry technique

2002 ◽  
Vol 2 (5-6) ◽  
pp. 47-55
Author(s):  
N.-S. Park ◽  
H. Park
Keyword(s):  
Particle Image Velocimetry ◽  
Particle Image ◽  
Velocity Fields ◽  
Local Velocity ◽  
Mixing Condition ◽  
Particle Image Velocimetry Technique ◽  
Velocity Gradients ◽  
Image Velocimetry ◽  
Current Design ◽  
G Value

Recognizing the significance of factual velocity fields in a rapid mixer, this study focuses on analyzing local velocity gradients in various mixer geometries with particle image velocimetry (PIV) and comparing the results of the analysis with the conventional G-value, for reviewing the roles of G-value in the current design and operation practices. The results of this study clearly show that many arguments and doubts are possible about the scientific correctness of G-value, and its current use. This is because the G-value attempts to represent the turbulent and complicated factual velocity field in a jar. Also, the results suggest that it is still a good index for representing some aspects of mixing condition, at least, mixing intensity. However, it cannot represent the distribution of velocity gradients in a jar, which is an important factor for mixing. This study as a result suggests developing another index for representing the distribution to be used with the G-value.

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